Asymptotic behavior of positive radial solutions to elliptic equations approaching critical growth

Abstract

We study the asymptotic behavior of radially symmetric solutions to the subcritical semilinear elliptic problem -∆u = u N+2/N-2 / [log(e + u)]α in Ω = BR(0) ⊂ ℝN, u > 0, in Ω, u = 0, on ∂Ω, as α → 0+. Using asymptotic estimates, we prove that there exists an explicitly defined constant L(N, R) > 0, only depending on N and R, such that lim supα→0+ αuα(0)2/[log(e + uα(0))]1+ α(N+2)/2 ≤ L(N, R) ≤ 2* lim infα→0+ αuα(0)2/[log(e + uα(0))]α(N-4)/2