Advances in Difference Equations
Volume 2007 (2007), Article ID 031640, 10 pages
doi:10.1155/2007/31640
Research Article
Eigenvalue Problems for Systems of Nonlinear Boundary Value Problems on Time Scales
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
Recommended by Kanishka Perera
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.