An application of topological transversality to non-positive higher order difference equations
type: Item
instance of: scholarly article
title: An application of topological transversality to non-positive higher order difference equations
zbMATH Open document ID: 0931.39002
DOI: 10.1016/S0096-3003(98)00005-8
author: Ravi P. Agarwal
author: Fu-Hsiang Wong
published in: Applied Mathematics and Computation
publication date: 2000-02-22T00:00:00Z
review text: The authors provide sufficient conditions on the non-positive function \(f(i,u_1,\ldots,u_{n-1})\) so that the boundary value problem given by \[ \Delta^n u(i)+\mu f(i,u(i),\Delta u(i),\ldots,\Delta^{n-2}u(i))=0, \] with boundary conditions \[ \Delta^m u(0)=0,\;0\leq m\leq n-3, \quad \alpha\Delta^{n-2}u(0)-\beta\Delta^{n-1} u(0)=0, \] \[ \gamma\Delta^{n-2} u(T+1)+\delta\Delta^{n-1} u(T+1)=0, \] has at least one positive solution. The topological transversality approach used here relies on a priori bounds on the solutions.
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 1311099
zbMATH Keywords: non-positive higher order boundary value problem
zbMATH Keywords: positive solutions
zbMATH Keywords: operator equations
zbMATH Keywords: a priori bounds
zbMATH Keywords: fixed point
zbMATH Keywords: difference equations
zbMATH Keywords: topological transversality
reviewed by: Rémi Vaillancourt
MaRDI profile type: Publication
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full work available at URL: s0096-3003(98)00005-8
OpenAlex ID: W2165098639
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description: scientific article; zbMATH DE number 1311099