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

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.