Advances in Difference Equations
Volume 2007 (2007), Article ID 31640, 10 pages
doi:10.1155/2007/31640
Research Article

Eigenvalue Problems for Systems of Nonlinear Boundary Value Problems on Time Scales

M. Benchohra,1 J. Henderson,2 and S. K. Ntouyas3

1Laboratoire de Mathématiques, Université de Sidi Bel Abbès, BP 89, 22000 Sidi Bel Abbès, Algeria
2Department of Mathematics, Baylor University, Waco, TX 76798, USA
3Department of Mathematics, University of Ioannina, Ioannina 45110, Greece

Received 28 June 2007; Accepted 19 November 2007

Academic Editor: Kanishka Perera

Copyright © 2007 M. Benchohra et al. 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.

Abstract

Values of λ are determined for which there exist positive solutions of the system of dynamic equations, uΔΔ(t)+λa(t)f(v(σ(t)))=0, vΔΔ(t)+λb(t)g(u(σ(t)))=0, for t∈[0,1]T, satisfying the boundary conditions, u(0)=0=u(σ2(1)), v(0)=0=v(σ2(1)), where T is a time scale. A Guo-Krasnosel'skii fixed point-theorem is applied.