Multiplicity of solutions for Neumann problems resonant at any eigenvalue
type: Item
instance of: scholarly article
title: Multiplicity of solutions for Neumann problems resonant at any eigenvalue
zbMATH Open document ID: 1296.35040
DOI: 10.1215/21562261-2642386
author: Leszek Gasiński
author: Nikolaos S. Papageorgiou
published in: Kyoto Journal of Mathematics
publication date: 2014-06-25T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kjm/1401741278
review text: The authors consider the following semilinear Neumann problem \[ \begin{cases} -\Delta u(z)=f(z,u(z)) & \text{in}\;\Omega,\\ \dfrac{\partial u}{\partial n}=0 & \text{on}\;\partial\Omega, \end{cases} \] where \(\Omega\subset {\mathbb R}^N\) is a bounded domain with a \(C^2\)-smooth boundary. The reaction term \(f(z,u)\) is supposed to be resonant both at \(\pm\infty\) and at zero with respect to any eigenvalue of the negative Neumann Laplacian. Using the reduction method and Morse theory, the authors show that the problem considered has at least two nontrivial smooth solutions.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6308332
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: Neumann problem
zbMATH Keywords: multiplicity
zbMATH Keywords: Morse theory
Wikidata QID: Q112251795
MaRDI profile type: Publication
OpenAlex ID: W2082157469
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description: scientific article; zbMATH DE number 6308332