On a \(p\)-Laplace Neumann problem with asymptotically asymmetric perturbations
type: Item
instance of: scholarly article
title: On a \(p\)-Laplace Neumann problem with asymptotically asymmetric perturbations
zbMATH Open document ID: 1157.35354
DOI: 10.1016/S0362-546X(01)00835-5
author: Mohssine Alif
author: Pierpaolo Omari
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-09-30T00:00:00Z
review text: The present paper deals with the elliptic problem of the form \[ \begin{gathered} -\Delta_p u= f(u)- h(x)\quad\text{in }\Omega,\\ {\partial \over\partial\nu}= 0\;\text{on}\;\partial\Omega,\end{gathered} \] where \(\Omega\subset\mathbb R^N\) is a bounded domain, \(\Delta_p\) is the \(p\)-Laplacian, \(p> 1\), \(h\in L^\infty(\Omega)\), \(f\in C(\mathbb R,\mathbb R)\). The goal of the authors is to improve and extend to the \(p\)-Laplacian well-known result for the Laplacian, in the case when \(f\) exhibits an asymmetric behaviour at infinity and may interact with the Dancer-Fučik spectrum.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1809997
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: asymmetric behaviour
zbMATH Keywords: Dancer-Fučik spectrum
MaRDI profile type: Publication
cites work: Equivalent Norms for Sobolev Spaces
cites work: Landesman-lazer conditions and quasilinear elliptic equations
cites work: On the antimaximum principle and the Fučik spectrum for the Neumann \(p\)-Laplacian
cites work: The beginning of the Fučik spectrum for the \(p\)-Laplacian
cites work: A nodal domain property for the p-Laplacian
cites work: Existence and localization of solution for second order elliptic BVP in presence of lower and upper solutions without any order
cites work: C1 + α local regularity of weak solutions of degenerate elliptic equations
cites work: On the first curve of the Fučik spectrum of an elliptic operator
cites work: Strongly nonlinear second-order ODE's with unilateral conditions
cites work: On a Semilinear Elliptic Neumann Problem with Asymmetric Nonlinearities
cites work: Existence and localization of solutions of second order elliptic problems using lower and upper solutions in the reversed order
cites work: Remarks on some quasilinear elliptic equations
cites work: Linear and quasilinear elliptic equations
cites work: Boundary regularity for solutions of degenerate elliptic equations
cites work: Nonresonance Conditions on the Potential for a Second-Order Periodic Boundary Value Problem
cites work: A strong maximum principle for some quasilinear elliptic equations
cites work: A Neumann problem with asymmetric nonlinearity and a related minimizing problem
description: scientific article; zbMATH DE number 1809997