Asymptotic behavior of positive radial solutions to elliptic equations approaching critical growth
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Date
2020-11-18
Authors
Pardo, Rosa
Sanjuan, Arturo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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
Description
Keywords
A priori bounds, Positive solutions, Semilinear elliptic equations, Dirichlet boundary conditions, Growth estimates, Subcritical nonlinearites
Citation
Pardo, R., & Sanjuán, A. (2020). Asymptotic behavior of positive radial solutions to elliptic equations approaching critical growth. <i>Electronic Journal of Differential Equations, 2020</i>(114), pp. 1-17.
Rights
Attribution 4.0 International