Asymptotic behavior of positive radial solutions to elliptic equations approaching critical growth
MetadataShow full metadata
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
CitationPardo, R., & Sanjuán, A. (2020). Asymptotic behavior of positive radial solutions to elliptic equations approaching critical growth. Electronic Journal of Differential Equations, 2020(114), pp. 1-17.
This work is licensed under a Creative Commons Attribution 4.0 International License.