Convergence for a planar elliptic problem with large exponent Neumann data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:502

Article

Fourti, Habib^1,2 

[1] Univ Monastir, Fac Sci, Monastir 5019, Tunisia

[2] Univ Sfax, Fac Sci, Lab LR 13 ES 21, Sfax 3000, Tunisia

关键词: Nonlinear boundary value problem;    Large exponent;    Asymptotic analysis;    Concentration of solutions;   

DOI  :  10.1016/j.jmaa.2021.125200

来源: Elsevier

【 摘 要 】

We study positive solutions u(p) of the nonlinear Neumann elliptic problem Delta u = u in Omega, partial derivative u/partial derivative nu=vertical bar u vertical bar(p-1)u on partial derivative Omega, where Omega is a bounded open smooth domain in R-2. We investigate the asymptotic behavior of families of solutions u(p) satisfying an energy bound condition when the exponent pis getting large. Inspired by the work of Davila-del Pino-Musso [8], we prove that upis developing m peaks x(i) is an element of partial derivative Omega, in the sense u(p)(p)/integral(partial derivative Omega) u(p)(p) approaches the sum of m Dirac masses at the boundary and we determine the localization of these concentration points. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free