Existence of multiple solutions with precise sign information for superlinear Neumann problems
type: Item
instance of: scholarly article
title: Existence of multiple solutions with precise sign information for superlinear Neumann problems
zbMATH Open document ID: 1188.35057
author: Nikolaos S. Papageorgiou
author: Vasile Staicu
author: Sergiu Aizicovici
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2009-09-25T00:00:00Z
review text: The authors consider a nonlinear Neumann problem involving \(p\)-Laplacian operator and a \((p-1)\) superlinear growth near infinity. They establish the existence of multiple constant sign solutions and nodal solutions by variational methods with truncation techniques and the use of ordered pairs of upper and lower solutions. Finally the semilinear case has been also considered.
reviewed by: Mohammed Bouchekif
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 5607376
zbMATH Keywords: Neumann problem
zbMATH Keywords: p-laplacian
zbMATH Keywords: constant sign solutions
zbMATH Keywords: nodal solutions
zbMATH Keywords: critical point theory
zbMATH Keywords: critical groups
MaRDI profile type: Publication
full work available at URL: s10231-009-0096-7
OpenAlex ID: W1978574750
cites work: The spectrum and an index formula for the Neumann \(p\)-Laplacian and multiple solutions for problems with a crossing nonlinearity
cites work: Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints
cites work: Existence of infinitely many weak solutions for a Neumann problem
cites work: A multiplicity theorem for the Neumann \(p\)-Laplacian with an asymmetric nonsmooth potential
cites work: Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
cites work: On a superlinear elliptic \(p\)-Laplacian equation.
cites work: Q4379821
cites work: Three solutions to a Neumann problem for elliptic equations involving the \(p\)-Laplacian
cites work: Q3140494
cites work: Sign-changing and multiple solutions for the \(p\)-Laplacian
cites work: Variational methods for non-differentiable functionals and their applications to partial differential equations
cites work: Infinite dimensional Morse theory and multiple solution problems
cites work: Optimization and nonsmooth analysis
cites work: The beginning of the Fučik spectrum for the \(p\)-Laplacian
cites work: Q3254057
cites work: Multiplicity Results for Nonlinear Neumann Problems
cites work: SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS
cites work: Q4828517
cites work: Q5312447
cites work: \(W^{1,p}\) versus \(C^1\) local minimizers and multiplicity results for quasilinear elliptic equations.
cites work: Multiple solutions of constant sign for nonlinear nonsmooth eigenvalue problems near resonance
cites work: Eigenvalue problems for the \(p\)-Laplacian
cites work: Every superposition operator mapping one Sobolev space into another is continuous
cites work: Critical point theory and Hamiltonian systems
cites work: Multiple nontrivial solutions for nonlinear eigenvalue problems
cites work: Existence and multiplicity of solutions for Neumann problems
cites work: A multiplicity theorem for problems with the \(p\)-Laplacian
cites work: Solution of nonlinear equations having asymptotic limits at zero and infinity.
cites work: A strong maximum principle for some quasilinear elliptic equations
cites work: On existence and multiplicity of solutions of Neumann boundary value problems for quasi-linear elliptic equations
cites work: Construction of pseudo-gradient vector field and sign-changing multiple solutions involving \(p\)-Laplacian
cites work: On sign-changing and multiple solutions of the \(p\)-Laplacian.
DOI: 10.1007/S10231-009-0096-7
description: scientific article; zbMATH DE number 5607376