Multiplicity of nontrivial solutions for a critical degenerate Kirchhoff type problem
type: Item
instance of: scholarly article
title: Multiplicity of nontrivial solutions for a critical degenerate Kirchhoff type problem
zbMATH Open document ID: 1378.35141
author: Zhisu Liu
author: Chun-Hong Zhang
published in: Applied Mathematics Letters
publication date: 2017-10-06T00:00:00Z
review text: The paper is concerned with the Kirchhoff type problem with critical growth \[ \begin{cases} -M\left(\displaystyle\int_{\Omega}|\nabla u|^2\,dx\right)\Delta u=\lambda |u|^2 u+|u|^4u,\,\,\,\text{in}\,\,\,\Omega,\\ u=0,\,\,\,\text{on}\,\,\,\partial\Omega, \end{cases}\tag{P} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^3\), \(M\in C(\mathbb{R}^+,\mathbb{R})\) and \(\lambda >0\). By using the contraction-compactness principle and an abstract critical point theorem, the authors investigate the existence and multiplicity of nontrivial solutions for problem (P), when \(\lambda\) belongs to some neighborhood of the eigenvalue of the nonlinear operator \(-M(\int_{\Omega}|\nabla u|^2\,dx)\Delta\).
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 6787228
zbMATH Keywords: degenerate Kirchhoff type equation
zbMATH Keywords: critical growth
zbMATH Keywords: multiplicity of solutions
reviewed by: Rodica Luca
MaRDI profile type: Publication
full work available at URL: j.aml.2017.01.016
OpenAlex ID: W2588051485
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DOI: 10.1016/J.AML.2017.01.016
description: scientific article