Existence and comparison results for difference \(\phi\)-Laplacian boundary value problems with lower and upper solutions in reverse order
type: Item
instance of: scholarly article
title: Existence and comparison results for difference \(\phi\)-Laplacian boundary value problems with lower and upper solutions in reverse order
zbMATH Open document ID: 0995.39003
author: Alberto Cabada
author: Victoria Otero-Espinar
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-10-23T00:00:00Z
review text: For a strictly increasing \(\varphi:\mathbb{R} \to\mathbb{R}\) with Lipschitzian \(\varphi^{-1}\) and a negative parameter \(M\) with small \(|M |\) the difference equation \(-\Delta [\varphi(\Delta u(k))]+ Mu(k+1)= \sigma (k)\) is studied under various boundary conditions. In particular existence, uniqueness and comparison results are derived. Generalizations to a difference equation with a second nonlinearity are pointed out.
reviewed by: Lothar Berg
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1749667
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: difference equation
zbMATH Keywords: boundary value problems
zbMATH Keywords: comparison principles
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7783
OpenAlex ID: W2094458903
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DOI: 10.1006/JMAA.2001.7783
description: scientific article; zbMATH DE number 1749667