Sign-changing solutions for \(p\)-biharmonic equations with Hardy potential
type: Item
instance of: scholarly article
title: Sign-changing solutions for \(p\)-biharmonic equations with Hardy potential
zbMATH Open document ID: 1317.35070
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-03-27T00:00:00Z
review text: The paper under review is concerned with the existence of nodal solutions for a class of \(p\)-biharmonic equations with Hardy potential and Dirichlet boundary condition. By means of variational arguments, the authors establish the existence of a sign-changing solution for small positive values of the parameter. The proof is essentially based on the method of invariant sets of descending flows. One of the key points is to construct a vector field that keeps the positive and negative cones invariant.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35J58
Mathematics Subject Classification ID: 35J30
Mathematics Subject Classification ID: 35B38
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6420047
zbMATH Keywords: sign-changing solutions
zbMATH Keywords: \(p\)-biharmonic equations
zbMATH Keywords: Hardy potential
zbMATH Keywords: variational methods
zbMATH Keywords: Dirichlet boundary condition
author: Yisheng Huang
author: Xiangqing Liu
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.10.044
OpenAlex ID: W4254904026
cites work: Nodal solutions of a p-Laplacian equation
cites work: Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
cites work: Explicit constants for Rellich inequalities in \(L_p(\Omega)\)
cites work: Invariant sets of descending flow in critical point theory with applications to nonlinear differential equations
cites work: Nonlinear biharmonic equations with Hardy potential and critical parameter
cites work: Multiple and sign-changing solutions for a class of semilinear biharmonic equation
cites work: Nonuniformly nonlinear elliptic equations of \(p\)-biharmonic type
cites work: Nodal solutions to superlinear biharmonic equations via decomposition in dual cones
cites work: Existence results for some fourth-order nonlinear elliptic problems of local superlinearity and sublinearity.
cites work: Existence results for some fourth-order nonlinear elliptic problems
cites work: Multiple nontrivial solutions for some fourth-order semilinear elliptic problems
cites work: Sign-changing solutions for some fourth-order nonlinear elliptic problems
DOI: 10.1016/J.JMAA.2013.10.044
description: scientific article; zbMATH DE number 6420047