Constant-sign and nodal solutions for a Neumann problem with \(p\)-Laplacian and equi-diffusive reaction term
type: Item
instance of: scholarly article
title: Constant-sign and nodal solutions for a Neumann problem with \(p\)-Laplacian and equi-diffusive reaction term
zbMATH Open document ID: 1268.35036
author: Salvatore A. Marano
author: Nikolaos S. Papageorgiou
published in: Topological Methods in Nonlinear Analysis
publication date: 2012-09-05T00:00:00Z
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6077382
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: Neumann problem
zbMATH Keywords: constant-sign solutions
zbMATH Keywords: nocal solutions
zbMATH Keywords: truncations
zbMATH Keywords: sub- and super-solutions
zbMATH Keywords: critical groups
reviewed by: Lubomira Softova
MaRDI profile type: Publication
review text: The authors consider the problem NEWLINE\[NEWLINE -\Delta_pu=\lambda|u|^{p-2}u-f(x,u)\qquad\text{ in } \Omega, \qquad \frac{\partial u}{\partial n}=0 \quad \text{ on } \partial\Omega. NEWLINE\]NEWLINE It is established existence of both constant and sign-changing (namely, nodal) solutions to a Neumann boundary-value problem with \(p\)-Laplacian and reaction term depending on a positive parameter \(\lambda.\) The proofs make use of sub- and super-solution techniques as well as critical point theory.
description: scientific article; zbMATH DE number 6077382