Calculating critical groups of solutions for elliptic problem with jumping nonlinearity
type: Item
instance of: scholarly article
title: Calculating critical groups of solutions for elliptic problem with jumping nonlinearity
zbMATH Open document ID: 1012.35022
DOI: 10.1016/S0362-546X(01)00139-0
author: Shaoping Wu
author: Jia-Quan Liu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-06-27T00:00:00Z
review text: The authors consider a semilinear elliptic equation of the form \[ \begin{cases} \Delta u+g(x,u)= 0\quad & \text{in }\Omega,\\ u=0\quad & \text{on } \partial\Omega, \end{cases}\tag{1} \] where \(\Omega\) is a bounded domain, \(g(x,u)\) is a given function. They calculate the critical groups for the trivial critical point. Existence of nontrivial solutions is obtained as a consequence through the Morse relation.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B38
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1761020
zbMATH Keywords: existence
zbMATH Keywords: trivial critical point
zbMATH Keywords: Morse relation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1761020