Asymptotic behavior at infinity of solutions of the Emden–Fowler type equation / 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.
