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• W2994392709 abstract "We study positive solutions $u_p$ of the nonlinear Neumann elliptic problem $Delta u =u$ in $Omega $, $partial u/partialnu = |u|^{p-1}u$ on $partialOmega$, where $Omega $ is a bounded open smooth domain in $mathbb{R}^2$. We investigate the asymptotic behavior of families of solutions $u_p$ satisfying an energy bound condition when the exponent $p$ is getting large. Inspired by the work of Davila-del Pino-Musso cite{DavilaDM}, we prove that $u_p$ is developing $m$ peaks $x_iinpartial Omega$, in the sense $u_p^p/int_{partial Omega}u_p^p$ approaches the sum of $m$ Dirac masses at the boundary and we determine the localization of these concentration points." @default.
• W2994392709 created "2019-12-13" @default.
• W2994392709 creator A5050805677 @default.
• W2994392709 date "2019-11-29" @default.
• W2994392709 modified "2023-09-27" @default.
• W2994392709 title "Convergence for a planar elliptic problem with large exponent Neumann data" @default.
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