Asymptotic behavior at infinity for solutions of Emden–Fowler type equations / M. D. Surnachev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. ? 2. P. 53-56 Moscow Univ. Math. Bulletin. Vol. 64, N 2, 2009. P. 67-69].

The semilinear equation \Delta u=|u|^{\sigma-1}u is considered in the exterior of a ball in \mathbb{R}^n,\ n\geq 3. It is shown that if the exponent \sigma is greater than a "critical" value (=\frac{n}{n-2}), then for x\to\infty the leading term of the asymptotics of any solution is a linear combination of derivatives of the fundamental solution. It is shown that solutions with the indicated leading term in asymptotics of such a type exist.

Key words: semilinear, asymptotics, Emden–Fowler equations, Kondrat'ev spaces, critical exponent, supercritical range.