Semilinear Robin problems resonant at both zero and infinity
type: Item
instance of: scholarly article
title: Semilinear Robin problems resonant at both zero and infinity
zbMATH Open document ID: 1384.35029
author: Nikolaos S. Papageorgiou
author: Vicenţiu D. Rădulescu
published in: Forum Mathematicum
publication date: 2018-01-12T00:00:00Z
review text: Given a bounded domain \(\Omega \subseteq \mathbb{R}^N\) with a \(C^2\)-boundary \(\partial \Omega\), the authors consider the following semilinear Robin problem \[ -\Delta u(z)=f(z,u(z)) \quad \text{in }\Omega, \qquad \frac{\partial u}{\partial n}+\beta(z)u=0 \quad\text{on }\partial \Omega,\tag{1} \] where the nonlinearity \(f:\Omega\times \mathbb{R}\to\mathbb{R}\) is measurable in the first argument, continuously differentiable with respect to the second variable and the boundary function \(\beta\) belongs to \(W^{1,\infty}(\partial \Omega)\) such that \(\beta(z) \geq 0\) for all \(z \in \partial \Omega\). Applying variational methods and critical groups, the authors prove the existence of at least two nontrivial smooth solutions of problem (1) under certain resonance conditions at \(\pm\infty\) and at zero.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6825367
zbMATH Keywords: semilinear Robin problem
zbMATH Keywords: variational methods
zbMATH Keywords: critical groups
MaRDI profile type: Publication
full work available at URL: forum-2016-0264
OpenAlex ID: W2908518760
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DOI: 10.1515/FORUM-2016-0264
description: scientific article; zbMATH DE number 6825367