Alexander KRASNOSEL'SKII

Researcher at the Laboratory since October 2006

---

• Institute for Information Transmission Problems,
• Russian Academy of Sciences,
• 19 Bolshoi Karetny lane, 101447, Moscow, Russia
• Tel: 7 (495) 420-59-39, Fax: 7 (495) 650-05-79, Mob.: 7 (916) 494-15-76
• E-Mails: sashaamk@iitp.ru and krasnoselskii@gmail.com
• Web: http://www.krasnoselskii.iitp.ru/

RESEARCH INTERESTS

General nonlinear analysis;
Functional analysis, operator equations;
Boundary value problems for ordinary and partial differential equations;
Bifurcation theory, nonlinear resonance;
System analysis (control theory, desynchronized systems, systems with hysteresis);
Numerical methods.

PUBLICATIONS

More than 150 publications and 2 monographs (Lists with texts: Russian and English).
One of them, "Asymptotics of Nonlinearities and Operator Equations" was published in Russian by Nauka, 1992 and in English by Birkhauser, 1995.

Selected publications

1. Krasnosel'skii A.M.
   Remarks on fixed points of monotonous operators,
   Uspekhi Mat. Nauk, 32, 6, 257-258 (1977) [Russian]
2. Krasnosel'skii A.M.
   A priori estimates of the norms of solutions of scalar inequalities,
   Soviet Math. Dokl., 19, 6, 1481-1485 (1978)
3. Krasnosel'skii A.M.
   New a priori estimates of two-point boundary problem solutions and its applications,
   Sibirskii Math. Journal, 21, 1, 115-124 (1980) [Russian]
4. Krasnosel'skii A.M.
   Frequency criteria in the problem on forced oscillations in control systems,
   Automation and Remote Control, 41, 9, 1203-1209 (1981)
5. Krasnosel'skii M.A., Kozyakin V.S., Krasnosel'skii A.M., Pokrovskii A.V.
   On dynamics of regulation system with number of nonlinearities,
   Proc. 2nd International Conference on Differential Equations, Russe, Bulgaria, 1, 366-376 (1982) [Russian]
6. Krasnosel'skii A.M., Yumagulov M.G.
   Bifurcation values of parameters in problem on forced oscillations in automated regulation systems,
   Dokl. Acad. Nauk Tajik SSR, 11, 679-682 (1983) [Russian]
7. Krasnosel'skii A.M.
   Forced periodic oscillations in complex nonlinear system,
   Automation and Remote Control, 44, 10, 1301-1306 (1984)
8. Krasnosel'skii A.M.
   On problem on forced oscillations in nonlinear control systems,
   Engnrg Cybernetics, 22, 5, 92-99 (1984)
9. Krasnosel'skii A.M.
   Forced periodic oscillations in nonlinear systems,
   Soviet Phys. Dokl., 29, 6, 438-440 (1984)
10. Krasnosel'skii A.M., Petrov D.I.
    On periodic oscillations in regulation systems with delays,
    Avtomatika i telemekhanika, 6, 169-171 (1984) [Russian]
11. Krasnosel'skii A.M.
    On periodic regimes in systems, described by equations of second order with delay,
    ``Heterogeneous system dynamics'', Moscow, Inst. for System Study, 156-162 (1984) [Russian]
12. Krasnosel'skii A.M., Krasnosel'skii M.A., Pokrovskii A.V.
    On application of guiding potential method to systems with hysteresis,
    ``Heterogeneous system dynamics'', Moscow, Inst. for System Study, 162-167 (1984) [Russian]
13. Krasnosel'skii A.M., Krasnosel'skii M.A.
    Large-amplitude cycles in autonomous systems with hysteresis,
    Soviet Math. Dokl., 32, 1, 14-17 (1985)
14. Krasnosel'skii A.M.
    One-side estimates in the problem of forced oscillations in nonlinear control systems,
    Soviet Math. Dokl., 32, 1, 74-77 (1985)
15. Krasnosel'skii A.M.
    Nonlocal theorems on forced oscillations in control systems,
    Proc. X International conf. on nonlinear oscillation (ICNO), Varna-Sofia, Bulg. Acad. Nauk, Bulgaria, 340-343 (1985) [Russian]
16. Krasnosel'skii A.M., Dement'eva A.M.
    On approximate solutions of some class of linear systems,
    ``Heterogeneous system dynamics'', Moscow, Inst. for System Study, 146-148 (1985) [Russian]
17. Krasnosel'skii A.M.
    One-side estimates in problems on forced periodic oscillations in multicontour systems,
    ``Heterogeneous system dynamics'', Moscow, Inst. for System Study, 27-32 (1985) [Russian]
18. Krasnosel'skii A.M.
    On stability of desynchronized multicomponent systems,
    Avtomatika i telemekhanika, 11, 170-171 (1985) [Russian]
19. Krasnosel'skii A.M.
    On some class of linear links with rational fractional transfer functions,
    Avtomatika i telemekhanika, 11, 166-170 (1986) [Russian]
20. Bobylev N.A., Boltyanskii V.G., Krasnosel'skii A.M. and colleagues,
    Mathematical system theory,
    monograph, Moscow, Nauka, 1986, 1-253 [Russian]
21. Krasnosel'skii A.M.
    New theorems on forced periodic oscillations in nonlinear control systems,
    Appl. Math. & Mech., 50, 2, 165-170 (1987)
22. Grachev N.A., Dement'eva A.M., Krasnosel'skii A.M., Petrov D.I.,
    Remarks on harmonic balance method in problem of forced oscillations in multilinked systems,
    ``Heterogeneous system dynamics'', Moscow, Inst. for System Study, 6, 68-71 (1987) [Russian]
23. Bobylev N.A., Krasnosel'skii A.M., Krasnosel'skii M.A., Pokrovskii A.V., Vladimirov A.A.,
    Functional analysis and dynamics of nonlinear control systems,
    Proc. X World congr. IFAC, Munich, Germany, 112-117 (1987).
    Selected Papers from 10th Triennal World Congress of the IFAC-1987, Munich, West Germany. Oxford, UK: Pergamon, 8, 11-15 (1988)
24. Krasnosel'skii A.M.
    Boundary problems for equations at resonance,
    Proc. 3d International Conf. on Diff. Equ., Ruse, Bulgaria, 1, 207-210 (1987) [Russian]
25. Krasnosel'skii A.M.
    Forced oscillations in system with hysteresis nonlinearities,
    Dokl. Acad. Nauk SSSR, 292, 5, 1078-1082 (1987) [Russian]
26. Krasnosel'skii A.M.
    Directional corrections in harmonic balance method,
    Sov. Phys. Dokl., 32, 6, 441-443 (1988)
27. Krasnosel'skii A.M.
    Conditions of applicability of Fredholm theorems in analysis of forced oscillations in nonlinear control systems,
    Avtomatika i telemekhanika, 3, 162-164 (1988) [Russian]
28. Bobylev N.A., Krasnosel'skii A.M., Krasnosel'skii M.A.
    Stability of periodic oscillations and the possibility of obtaining them by the method of harmonic balance,
    Avtomatika i telemekhanika, 5, 179-181 (1989) [Russian]
29. Krasnosel'skii A.M., Dement'eva A.M., Yumagulov M.G.
    Periodic problem operator for a first order equation,
    Dokl. Acad. Nauk Tajik SSR, 12, 802-805 (1989) [Russian]
30. Bobylev N.A., Krasnosel'skii A.M., Krasnosel'skii M.A., Pokrovskii A.V.
    On some new ideas in nonlinear analysis,
    ``Nonlinear boundary problems'', Kiev, 1, 22-26 (1989)
31. Krasnosel'skii A.M., Dement'eva A.M., Yumagulov M.G.
    On approximate construction of periodic solutions of first order nonlinear equation,
    Dokl. Acad. Nauk Tajik SSR, 3, 712-715 (1990) [Russian]
32. Krasnosel'skii A.M. and colleagues,
    The new results in the theory of periodic oscillation in nonlinear control systems,
    Proc. XI World Congr. IFAC, Tallinn, 6, 50-55 (1990)
33. Krasnosel'skii A.M.
    Joint norm of operators and the study of nonlinear problems,
    Ukrainian Math. J., 42, 12, 1442-1452 (1990)
34. Krasnosel'skii A.M.
    On a method of analysis of resonance problems,
    Nonlinear Analysis, Theory, Methods & Applications, 16, 4, 321-345 (1991)
35. Krasnosel'skii A.M., Krasnosel'skii M.A.
    On some class of equations with potential operators,
    Note di Mat., Italy, XI, 237-245 (1991)
36. Krasnosel'skii A.M., Appell J.
    New theorems on asymptotic bifurcation point,
    Nonlinear Analysis, Theory, Methods & Applications, 18, 269-276 (1992)
37. Krasnosel'skii A.M.
    Large-amplitude oscillations in systems with saturation,
    Sov. Phys. Dokl., 32, 6, 419-421 (1992)
38. Krasnosel'skii A.M.
    Asymptotics of nonlinearities and operator equations, monograph, Moscow, Nauka, 1992 [Russian]
    English translation in: ser. "Operator Theory", vol. 76, Birkhauser, 1995,
39. Krasnosel'skii A.M.
    On bifurcation points of equations with Landesman-Lazer type nonlinearities,
    Nonlinear Analysis. Theory, Methods & Applications, 18, 12, 1187-1199 (1992)
40. Krasnosel'skii A.M., Krasnosel'skii M.A., Kuznetsov N.A.
    Nonlinear systems with incomplete corrections and their stability,
    Sov. Phys. Dokl., 36, 5, 356-357 (1992)
41. Krasnosel'skii A.M., Krasnosel'skii M.A., Mawhin J.
    On some conditions of existence of forced periodic oscillations,
    Differential and Integral Equations, 5, 6, 1267-1273 (1992)
42. Krasnosel'skii A.M., Mawhin J.
    Remark on some type of bifurcation at infinity,
    Bull. de la Classe des Sci, Ac. Roy. de Belgique, III, #12, 293-297 (1992)
43. Krasnosel'skii A.M.
    On algebraic number of solutions of systems with Landesman-Lazer type nonlinearities,
    Adv. Math. Sci. & Appl., 2, #2, 391-395 (1993)
44. Krasnoselskii A.M.
    On nonlinear resonance in systems with hysteresis,
    ``Models in Hysteresis'', ed. A.Visintin, Pitman Res. Notes in Math. Ser., 286, Longman Sci. & Tech., 71-76 (1993)
45. Bobylev N.A., Dement'eva A.M., Krasnosel'skii A.M.
    On Poincare index in problems of optimization and control,
    Automation and Remote Control, 55, #2, 172-177 (1994)
46. Krasnosel'skii A.M., Krasnosel'skii M.A., Mawhin J., Pokrovskii A.V.
    Generalized guiding functions in a problem on high frequency forced oscillations,
    Nonlinear Analysis. Theory, Methods & Applications, 22, #2, 1357-1372 (1994)
47. Eirola T., Krasnosel'skii A.M., Krasnosel'skii M.A., Kuznetsov N.A., Nevanlinna~O.
    Incomplete corrections for linear systems with self-adjoint operators,
    Sov. Phys. Dokl., 39, #11 (1994)
48. Krasnosel'skii A.M.
    Nonresonance sectoral estimates in problems of forced oscillations in control systems,
    Automation and Remote Control, 55, #12, 1740-1744 (1994)
49. Krasnosel'skii A.M., Mawhin J.
    The index at infinity of some twice degenerate compact vector fields,
    Discrete and Continuous Dynamical Systems, 1, #2, 207-216 (1995)
50. Krasnosel'skii A.M., Mawhin J.
    On some higher order boundary value problems at resonance,
    Nonlinear Analysis. Theory, Methods & Applications, 24, #8, 1141-1148 (1995)
51. Krasnosel'skii A.M.
    On nonlinear resonance in systems with delays,
    Automation and Remote Control, 56, #2 (1995) 160-166
52. Eirola T., Krasnosel'skii A.M., Krasnosel'skii M.A., Kuznetsov N.A., Nevanlinna~O.
    Stability of systems with incomplete corrections,
    Nonlinear Analysis. Theory, Methods & Applications, 25, #7, 717-728 (1995)
53. Krasnosel'skii A.M., Sorine M.
    Discrete asinchronous iterations,
    Automation and Remote Control, 56, #11, 1557-1564 (1995)
54. Krasnosel'skii A.M., Krasnosel'skii M.A., Mawhin J.
    Differential inequalities in problems on forced nonlinear oscillations,
    Nonlinear Analysis. Theory, Methods & Applications, 24, #9-10, 1029-1036 (1995)
55. Bliman P.A., Krasnosel'skii A.M., Sorine M.
    Dither in systems with hysteresis,
    Res. Raport INRIA, 2690, 1-40 (1995)
56. Bliman P.A., Krasnosel'skii A.M., Sorine M., Vladimirov A.A.
    Forced oscillations in control systems with hysteresis,
    Doklady Mathematics, 53, #2, 312-315 (1996)
57. Bliman P.A., Krasnosel'skii A.M., Sorine M., Vladimirov A.A.
    Nonlinear resonance in systems with hysteresis,
    Nonlinear Analysis. Theory, Methods & Applications, 27, #5, 561-577 (1996)
58. Krasnosel'skii A.M.
    Asymptotic homogeneity of hysteresis operators,
    Zeitschrift fuer Angewandte Mathematik und Mechanik (ZAMM), 76, #2, 313-316 (1996)
59. Krasnosel'skii A.M.
    On forced oscillations in systems with even functional unbounded characteristics,
    Automation and Remote Control, 58 2, p.1, 27-36 (1997)
60. Krasnosel'skii A.M., Krasnosel'skii M.A.
    Vector fields in a product of spaces and applications to differential equations,
    Differential equations, 33, #1, 59-66 (1997)
61. Bliman P.-A., Krasnosel'skii A.M
    Periodic solutions of linear systems coupled with relay,
    Nonlinear Analysis, Theory, Methods & Applications, 30, #2, 687-696 (1997)
62. Krasnosel'skii A.M. and colleagues,
    Mark Alexandrovich Krasnosel'skii, obituary,
    Journal of Applied Mathematics and Stochastic Analysis, 10, #2, 119-126 (1997)
63. Bobylev N.A., Kloeden P., Kozyakin V.S., Krasnosel'skii A.M., Pokrovskii A.V., Sadovskii B.S.,
    In Memomriam Mark A.Krasnosel'skii,
    Mitteilungen der Gesellschaft für Angewandte Math. and Mech., 20, #1, 13-14 (1997)
64. Krasnosel'skii A.M., Krasnosel'skii M.A., Pokrovskii A.V.
    Hysteresis, Hysteron, Non-ideal relay,
    Encyclopaedia of Mathematics, Supplement Volume I, Editor-in-Chief: Prof. Dr. M. Hazewinkel, Kluwer Acad. Publ., p.310, p.384 (1997)
65. Diamond P., Kloeden P.E., Krasnosel'skii A.M., Pokrovskii A.V.
    Bifurcations at infinity for equations in spaces of vector-valued functions,
    Journal of Australian Mathematical Society, Series A, 63, 263-280 (1997)
66. Bliman P.A., Krasnosel'skii A.M.
    Popov-like frequency criterion for existence of forced periodic oscillations
    Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, TM 12-7, 2467-2472 (1998)
67. Bliman P.A., Krasnosel'skii A.M.
    Popov criterion and forced periodic oscillations,
    Automation and Remote Control, 59, #4, p.1, 457-466 (1998)
68. Krasnosel'skii A.M., Rachinskii D.I.
    Numerical series,
    student manual, State Jewish Academy, 1998, 1-22 [Russian]
69. Krasnosel'skii A.M., Rachinskii D.I.
    Numerical sequence limit,
    student manual, State Jewish Academy, 1998, 1-24 [Russian]
70. Krasnosel'skii A.M., Mawhin J.
    Equations with sequences of solutions
    Modern methods in BVP, proceedings of the 10th Pontryagin conference, Voronezh, 1988, p.112 [Russian]
71. Kloeden P., Krasnosel'skii A.M.
    Twice degenerate equations in the spaces of vector-valued functions,
    Arab. J. Math. Sci. 4, #1, 1-28 (1998)
72. Bliman P.-A., Krasnosel'skii A.M.
    An extension of Popov criterion to multivariable time-varying nonlinear systems.
    Application to criterion for existence of stable limit cycles,
    Res. Raport INRIA no. 3512, 1-19 (1998)
73. Krasnosel'skii A.M.,
    On oscillations in resonant equations with complex nonlinearities,
    Proceedings of the 7th IEEE Mediterranean Conference on Control and Automation (MED99), Israel, 1231-1243 (1999)
74. Krasnosel'skii A.M.,
    Unbounded sequences of cycles in autonomous control systems,
    Automation and Remote Control, 60, #8, p.1, 1117-1125 (1999)
75. Krasnosel'skii A.M., Chernorutskii V.V.,
    Hopf bifurcations from equilibrium, generated by small nonlinear terms,
    Automation and Remote Control, 60, #9, p.1, 1237-1242 (1999)
76. Krasnosel'skii A.M., Rachinskii D.I.,
    Hopf bifurcations from infinity, generated by bounded nonlinear terms,
    Functional Differential Equations, 6, #3-4, 357-374 (1999)
77. Bliman P.-A., Krasnosel'skii A.M.,
    Popov absolute stability criterion for time-varying multivariable nonlinear systems,
    Proceedings of European Control Conference, Germany, Karlsruhe, #F888, 1-6, (1999)
78. Krasnosel'skii A.M., Mennicken R., Rachinskii D.I.,
    Hopf bifurcation generated by small nonlinear terms,
    Zeitschrift fuer Angewandte Mathematik und Mechanik (ZAMM), 80, S2, 289-290 (2000)
79. Krasnosel'skii A.M., Mawhin J.
    The index at infinity for some vector fields with oscillating nonlinearities,
    Discrete and Continuous Dynamical Systems, 6, #1, 165-174 (2000)
80. Kloeden P., Krasnosel'skii A.M.
    Oscillations in systems with asymptotically even nonlinearities,
    Journal of Applied Mathematics and Stochastic Analysis 13, 41-50 (2000)
81. Krasnosel'skii A.M., Rachinskii D.I.,
    Continua of Cycles in Hamiltonian Control Systems,
    Institute for Nonlinear Sciences, National University of Ireland, University College, Cork,
    report 00-001, 1-13 (2000)
82. Bliman P.-A., Krasnosel'skii A.M., Rachinskii D.I.,
    Sector Estimates of Nonlinearities and Existence of Cycles in Control Systems,
    Institute for Nonlinear Sciences, National University of Ireland, University College, Cork,
    report 00-002, 1-20 (2000)
83. Bliman P.-A., Krasnosel'skii A.M., Rachinskii D.I.,
    Sector estimates of nonlinearities and self-oscillation existence in control systems,
    Automation and Remote Control, 61, #6, p.1, 889-903 (2000)
84. Krasnosel'skii A.M., Rachinskii D.I.,
    On Hamiltonian Lurie systems,
    Automation and Remote Control, 61, 8, p.1, 1259-1262 (2000)
85. Krasnosel'skii A.M., Kuznetsov N.A., Rachinskii D.I.,
    Nonlinear Hopf bifurcations,
    Doklady Mathematics, 61, 3, 389-392 (2000)
86. Krasnosel'skii A.M., Kuznetsov N.A., Rachinskii D.I.,
    On resonant equations with unbounded nonlinearities,
    Doklady Mathematics, 62, 1, 44-48 (2000)
87. Krasnosel'skii A.M., Mawhin J.,
    Periodic solutions of equations with oscillating nonlinearities,
    Mathematical and Computer Modelling, 32, 1445-1455 (2000)
88. Krasnosel'skii A.M., McInerney J., Pokrovskii A.V.,
    Weak resonances in Hopf bifurcations for control systems with nonpolynomial nonlinearities,
    Doklady Mathematics, 62, 3, 432-437 (2000)
89. Krasnosel'skii A.M., Rachinskii D.I.,
    Continua of Cycles in Hamiltonian Control Systems,
    Automation and Remote Control, 62, 2 (2001) 227-235
90. Krasnosel'skii A.M., Rachinskii D.I.,
    On continua of cycles in systems with hysteresis,
    Doklady Mathematics, 63, 3, 243-248 (2001)
91. Krasnosel'skii A.M., Pokrovskii A.V.,
    On subharmonics bifurcation in equations with homogeneous nonlinearities,
    Discrete and Continuous Dynamical Systems, 7, #7, 100-114 (2001)
92. Krasnosel'skii A.M., Cross R., Pokrovskii A.V.,
    Time-dependent Preisach nonlinearities and their properties,
    Doklady Mathematics, 64, 3 (2001) 435-438
93. Bliman P.-A., Krasnosel'skii A.M., Rachinskii D.I.,
    On strong resonances for Hopf bifurcations in control systems
    Automation and Remote Control, 62 2 (2001) 1783-1802
94. Krasnosel'skii A.M., Rachinskii D.I.
    On existence of cycles for quasilinear ODE of higher order,
    Izvestija RAEN, ser. MMMIU, 5, 1-2, 143-151 (2001)
95. Krasnosel'skii A.M., Rachinskii D.I.
    Hopf bifurcations in systems with Preisach hysteresis,
    Abstracts of the 1st SIAM-EMS conference ``Applied Mathematics in our Changing World'', Berlin, 2001, p. 29
96. Krasnosel'skii A.M., Mennicken R., Rachinskii D.I.,
    Small periodic solutions generated by sublinear terms,
    Journal of Differential Equations, 179, 97-132 (2002)
97. Krasnosel'skii A.M., Rachinskii D.I.
    On existence of cycles in autonomous systems,
    Doklady Mathematics, 65, 3, (2002) 344-349
98. Krasnosel'skii A.M., Mennicken R., Rachinskii D.I.,
    Cycle stability for Hopf bifurcation, generated by sublinear terms,
    Mathematische Nachrichten, 235, 171-195 (2002)
99. Krasnosel'skii A.M., Kuznetsov N.A., Rachinskii D.I.,
    On resonant differential equations with unbounded nonlinearities,
    Journal for Analysis and Applications, 21, 3, 639-668 (2002)
100. Cross R., Krasnosel'skii A.M., Pokrovskii A.V.
     A time-dependent Preisach model,
     Physica B: Condensed Matter, 306, 1-4, 206-210 (2002)
101. Krasnosel'skii A.M., Rachinskii D.I.,
     On a bifurcation governed by hysteresis nonlinearity,
     Nonlinear Differential Equations and Applications, 9, 93-115 (2002)
102. Krasnosel'skii A.M., Rachinskii D.I., Schneider K.,
     Hopf bifurcations in resonans 2:1,
     Nonlinear Analysis. Theory, Methods & Applications, 52, 3, 943-960 (2003)
103. Krasnosel'skii A.M., Rachinskii D.I.
     Continua of cycles of higher-order equations,
     Differential Equations, 39, 12 1690-1702 (2003)
104. Krasnosel'skii A.M., Rachinskii D.I.
     On continuous branches of cycles in systems with nonlinearizable nonlinearities,
     Doklady Mathematics, 67, 2 (2003) 153-157
105. Krasnosel'skii A.M., Rachinskii D.I.
     On a nonlocal condition for the existence of cycles of hysteresis systems,
     Automation and Remote Control, 64, 2 (2003) 231-251
106. Krasnosel'skii A.M., Rachinskii D.I.
     Nonlocal theorems on Hopf bifurcations,
     Abstracts of international conference Kolmogorov and contemporary mathematics, Moscow, 2003, 67-68
107. Krasnosel'skii A.M., Rachinskii D.I.
     On global branches of cycles and Hopf byfurcations,
     Proceedings of international conference "Modern problems on functional analysis and differential equations", Voronezh, 2003, 159-161 [Russian]
108. Krasnosel'skii A.M., Pokrovskii A.V.
     Remark on Rotation of Bilinear Vector Fields,
     Preprint No. 04/2003 of the School of Mathematics, Applied Mathematics and Statistics,
     National University of Ireland, University College, Cork, 2003, 1-9
     
109. Krasnosel'skii A.M., Pokrovskii A.V.
     Subharmonics of large amplitudes in a semilinear Duffing oscillator,
     Doklady Mathematics, 68, 1 (2003) 84-88
110. Krasnosel'skii A.M., Rachinskii D.I.
     On continuous branches of twice periodic solutions of some PDE,
     Functional Differential Equations, 10, 1-2 (2003) 291-301
111. Krasnosel'skii A.M., Rachinskii D.I.
     Branching at infinity of solutions to equations with degeneration of multiplicity 2,
     Doklady Mathematics, Doklady Mathematics (Springer), 69, 1 (2004) 79-83
112. Krasnosel'skii A.M., Pokrovskii A.V., Rachinskii D.I.
     A comparison of guaranteed estimates for the rate of convergence of a class of iterative procedures,
     Automation and Remote Control, 65, 10 (2004) 1635-1640
     
113. Krasnosel'skii A.M., McInerney J., Pokrovskii A.V.
     Sinchronized double frequency oscillations in a class of weakly resonant systems,
     Nonlinear Analysis. Theory, Methods & Applications, 57, 7-8 (2004) 929-949
114. Krasnosel'skii A.M., Rachinskii D.I.
     Remark on Hopf Bifurcation Theorem,
     Mathematische Nachrichten, 272 (2004) 95-103
115. Krasnosel'skii A.M., Pokrovskii A.V.
     Large subharmonics of pendulum-like equations,
     in `The first 60 years of NONLINEAR ANALYSIS of JEAN MAWHIN`,
     Eds. M. Delgado, J.Lopez-Gomez, R.Ortega, A.Suarez, World Scientific Publishing, 2004, 103-116
116. Krasnosel'skii A.M., Rachinskii D.I.
     On a number of solution branches at asymptotic bifurcation point,
     Functional analysis and applications, 39, 3 (2005) 194-206
117. Krasnosel'skii A.M., Rachinskii D.I.
     On the number of branches of periodic solutions,
     EQUADIFF 2003, World Scientific Publishing, 2005, 246-248
118. Krasnosel'skii A.M., Rachinskii D.I.
     Bifurcation of forced periodic oscillations for equation with Preisach hysteresis,
     Journal of Physics: Conference Series, 22 (2005) 93-102
119. Krasnosel'skii A.M., Pokrovskii A.V.
     Dissipativity of nonresonant systems with ferromagnetic friction via a canonical example,
     Physica B: Condensed Matter, 372, 1-2 (2006) 13-16
120. Krasnosel'skii A.M., Pokrovskii A.V.
     Dissipativity of pendulum with ferromagnetic friction,
     Automation and Remote Control, 67, 2 (2006) 221-232
121. Krasnosel'skii A.M., Rachinskii D.I.
     Subharmonic bifurcation at infinity,
     Journal of Differential Equations, 226, 1 (2006) 30-53
122. Kozyakin V.S., Krasnosel'skii A.M., Rachinskii D.I
     On Arnold tongues in the problem of large-amlitude periodic trajectories,
     Doklady Mathematics, 74, 3 (2006) 821-827
123. Krasnosel'skii A.M., Pokrovskii A.V.
     topologically stable subharmonics of large periods and amplitudes,
     Differential equations, 43, 2 (2007) 1-28
124. Krasnosel'skii A.M., Pokrovskii A.V., Rachinskii D.I.
     Non-local Branches of Cycles, Bi-stability, and Mixed Mode Oscillation Phenomenon,
     Chaos, 18, 1, 015109 (2008)
125. Kozyakin V.S., Krasnosel'skii A.M., Rachinskii D.I
     Arnold tongues for bifurcation from infinity,
     Discrete and Continuous Dynamical Systems - Series S, 1, 1 (2008) 107-116
126. Krasnosel'skii A.M.
     Double degeneration in the problem on unbounded branches of forced oscillations,
     Doklady Mathematics, 77, 2 (2008) 170-174
127. Kozyakin V.S., Krasnosel'skii A.M., Rachinskii D.I.
     Asymptotics of Arnold tongues in problems at infinity,
     Discrete and Continuous Dynamical Systems - Series A, 20, 4 (2008) 989-1011
128. Krasnosel'skii A.M., Rachinskii D.I.
     Criterion of nonlinear resonance appearence in single-loop control system with saturation,
     Automation and Remote Control, 69, 8 (2008) 1297-1310
129. Krasnosel'skii A.M., Rachinskii D.I.
     On nonconnected unbounded sets of forced oscillations,
     Doklady Mathematics, 78, 1 (2008) 660-664
130. Krasnosel'skii A.M., Rachinskii D.I.
     Nontrivial bifurcations at infinity,
     Proceedings of the International Conference Differential equations and topology,
     dedicated to the 100th Anniversary of the birthday of L.S. Pontryagin, Moscow, 2008, 148-149 [Russian]
131. Krasnosel'skii A., Rachinskii D.
     Bifurcations to unbounded sequence of cyclic branches of solutions,
     Abstracts of the Fifth International Conference on Differential and Functional Differential Equations, DFDE2008, Moscow, Russia, August 17-24, 2008, 38-39
132. O'Ceallaigh S., Krasnosel'skii A., Pimenov A., Rachinskii D.
     Fold bifurcations and linear stability analysis in systems with Preisach hysteresis,
     sent to Proceedings of EQUADIFF 2007, World Scientific Publishing
133. Krasnosel'skii A.M.
     Unbounded branches of periodic oscillations,
     Differential equations (Differencialnye Uravneniya), 2009 [Russian], accepted
134. Krasnosel'skii A.M.
     Index at infinity and bifurcations of twice degenerate vector fields,
     sent to Topological Methods in Nonlinear Analysis

EDITORIALS

Member of the Editorial Board of Journal of Applied Mathematics and Stochastic Analysis http://www.hindawi.com/journals/jamsa/index.html
Member of the Editorial Board of "Automation and Remote Control" (Russia) http://www.ipu.ru/ [Russian], http://www.maik.ru/ [English]
Member of the Editorial Board of "Pollack Periodica" (Hungary) English, New International Journal for Engenineering and Information Sciences
Member of the Editorial Board of "International Journal of Differential Equations" http://www.hindawi.com/journals/ijde/

EDUCATION, DEGREES

EXPERIENCE

1990 - present
Institute of Information Transmission Problems, Russian Academy of Sciences
19 Bolshoi Karetny lane, Moscow, 101447, RUSSIA
Position: leading research analyst
Description of work:

• Investigation of nonlinear resonance phenomenon
  in abstract systems and boundary value problems of several types;
• Analysis of nonlinear oscillations in control systems;
• Research in degree theory;
• Analysis of bifurcation at infinity;
• Hopf bifurcations, auto-oscillations;
• Hysteresis;
• Desynchronized system study and numerical methods of analysis;
• Students and young researches supervision

1992 - 1998
Jewish State Academy, Department of Informatics
Position: head of the chair of analysis
Description of work:

• Lectures on mathematical analysis (calculus);
• Students supervision;
• Administrative functions

1992 - 1993
Moscow State University, Faculty of Computer Sciences and Cybernetycs
Leninskie Gory, Moscow, Russia
Position: associated professor
Description of work:

• Lectures in functional analysis (special course);
• Students supervision

1988 - 1990
Scientific-Industrial Association on Automated Control and Computer Processing
(NPO ASU ``Moskva'')
18, Bakhrushina, Moscow, 113054, Russia
Position: chairman of mathematic group in department of Moscow ecology
Description of work:

• Investigation of nonlinear resonance phenomenon in abstract
  systems and boundary value problems of several types;
• Numerical methods of the periodic regimes construction
  in nonlinear control systems;
• Modeling of the air pollution in Moscow;
• Ecological data base supervision

1976 - 1988
National Cardiology Research Center, Russian Academy of Medical Sciences
15a 3d Cherepkovskaja str, Moscow, Russia
Positions: researcher (1976-1981), research analyst (1981-1986), senior research analyst (1986-1988)
Description of work:

• Automated analysis of electrocardiograms;
• A priori estimates in boundary value problems;
• Mathematical modeling of various problems in cardiology;
• Analysis of applicability of harmonic balance method in
  the problem of forced oscillation in nonlinear systems;
• Medical data bases;
• Analysis of system with hysteresis (quiding functions, operator approach, modelling);
• Numerical methods in operator equation theory.

WORK IN OTHER COUNTRIES