Nonlinear perturbations of some non-invertible differential operators
type: Item
instance of: scholarly article
title: Nonlinear perturbations of some non-invertible differential operators
zbMATH Open document ID: 1240.34073
author: Alessandro Fonda
author: Rodica Toader
published in: Differential and Integral Equations
publication date: 2011-09-01T00:00:00Z
review text: The paper deals with problems of the type \(L\,u=N_{\lambda }\,u,\) where \(L\) is a non-invertible differential operator having compact resolvent and nonnegative spectrum and \(N_\lambda \) is a nonlinear operator depending continuously on a small parameter \(\lambda ,\) \(N_0=0.\) Assuming the existence of a pair of (possibly non-ordered) lower and upper solutions belonging to the kernel of \(L,\) the authors prove the existence of a solution for \(\lambda \) sufficiently small. Applications are given for a wide class of problems, ranging from ODEs to equations of parabolic and elliptic types, and equations involving the \(p\)-Laplacian operator. Also, interesting non-existence results are given.
reviewed by: Milan Tvrdý
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35J67
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 5944853
zbMATH Keywords: nonlinear perturbation
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: periodic problem
zbMATH Keywords: Neumann problem
zbMATH Keywords: Neumann-periodic problem
zbMATH Keywords: second order ODE
zbMATH Keywords: parabolic equation
zbMATH Keywords: elliptic equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5944853