Abstract and Applied Analysis

Abstract and Applied Analysis / 1997 / Article

Open Access

Volume 2 |Article ID 696821 | 9 pages | https://doi.org/10.1155/S1085337597000390

Existence of a positive solution for an nth order boundary value problem for nonlinear difference equations

Received26 Oct 1997

Abstract

The nth order eigenvalue problem: Δnx(t)=(1)nkλf(t,x(t)),t[0,T],x(0)=x(1)==x(k1)=x(T+k+1)==x(T+n)=0, is considered, where n2 and k{1,2,,n1} are given. Eigenvalues λ are determined for f continuous and the case where the limits f0(t)=limn0+f(t,u)u and f(t)=limnf(t,u)u exist for all t[0,T]. Guo's fixed point theorem is applied to operators defined on annular regions in a cone.

Copyright © 1997 Hindawi Publishing Corporation. 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.

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