On exterior Neumann problems with an asymptotically linear nonlinearity
type: Item
instance of: scholarly article
title: On exterior Neumann problems with an asymptotically linear nonlinearity
zbMATH Open document ID: 1174.35046
author: Tatsuya Watanabe
published in: Journal of Differential Equations
publication date: 2007-09-13T00:00:00Z
review text: The author studies the following semilinear elliptic problem in an exterior domain with the Neumann boundary condition \[ \begin{gathered} -\Delta u+ u+ f(u)\quad\text{in }\mathbb R^N\setminus \overline\Omega,\\ {\partial u\over\partial\nu}= 0\quad\text{on }\partial\Omega,\end{gathered}\tag{1} \] where \(\Omega\subset\mathbb R^N\) is an open bounded domain with \(\partial\Omega\in C^1\), \(N\geq 3\), and \(\nu\) is the interior unit normal vector on \(\partial\Omega\). The author is interested in the existence of a ground state solution of (1) and under the natural assumptions on \(f\) proves its existence. Moreover, the author shows that, when \(\Omega\) is a ball, a ground state solution not necessarily radially symmetric and gives also asymptotic profile of ground state solutions.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 5190775
zbMATH Keywords: exterior Neumann problems
zbMATH Keywords: asymptotically linear nonlinearity
zbMATH Keywords: ground state solutions
zbMATH Keywords: symmetry breaking phenomena
MaRDI profile type: Publication
full work available at URL: j.jde.2007.05.020
OpenAlex ID: W2017025981
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DOI: 10.1016/J.JDE.2007.05.020
description: scientific article; zbMATH DE number 5190775