Abstract and Applied Analysis
Volume 2 (1997), Issue 3-4, Pages 271-279

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

Johnny Henderson1 and Susan D. Lauer2

1Department of Mathematics, Auburn University, Auburn, Alabama 38649, USA
2Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088, USA

Received 26 October 1997

Copyright © 1997 Johnny Henderson and Susan D. Lauer. 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.


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.