Advances in Difference Equations
Volume 2007 (2007), Article ID 31640, 10 pages
doi:10.1155/2007/31640
Eigenvalue problems for systems of nonlinear boundary value problems on time scales
M. Benchohra1
, J. Henderson2
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
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.