Extremal solutions for the difference \(\phi\)-Laplacian problem with nonlinear functional boundary conditions
type: Item
instance of: scholarly article
title: Extremal solutions for the difference \(\phi\)-Laplacian problem with nonlinear functional boundary conditions
zbMATH Open document ID: 1001.39006
DOI: 10.1016/S0898-1221(01)00179-1
author: Alberto Cabada
publication date: 2002-06-13T00:00:00Z
review text: The paper deals with the difference equation \[ -\Delta[\phi(\Delta u_k)]=f(k,u_{k+1}),\quad k\in \{ 0,1,\dots,N-1\}, \] where \(f\) is continuous and \(\phi\) is continuous and strictly increasing and \(\phi(\mathbb{R})=\mathbb{R}\). The equation is studied together with functional boundary conditions that include Dirichlet, Neumann and mixed type as well as periodic conditions. Under some hypotheses the problem under consideration has at least one solution (resp. a unique solution, resp. an extremal solution). The construction of two monotone sequences that converge to the extremal solution is presented in details.
reviewed by: Dobiesław Bobrowski
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1755276
zbMATH Keywords: difference equation
zbMATH Keywords: \(\phi\)-Laplacian problem
zbMATH Keywords: nonlinear functional boundary conditions
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: extremal solution
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1755276