Open Access

Multiple nonnegative solutions for BVPs of fourth-order difference equations

Advances in Difference Equations20062006:089585

DOI: 10.1155/ADE/2006/89585

Received: 31 March 2006

Accepted: 18 September 2006

Published: 7 December 2006

Abstract

First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ4x(t-2) = a(t)f(x(t)),t [2, T], x(0) = x(T + 2) = 0, Δ2x(0) = Δ2x(T) = 0 are established by using the well-known Leggett-Williams fixed point theorem, and then, for arbitrary positive integer m, existence results for at least 2m-1 nonnegative solutions are obtained.

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Authors’ Affiliations

(1)
Department of Applied Mathematics, Lanzhou University of Technology

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Copyright

© Jian-Ping Sun 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.