Advances in Difference Equations
Volume 2008 (2008), Article ID 879140, 9 pages
doi:10.1155/2008/879140

Eigenvalue Problems for p-Laplacian Functional Dynamic Equations on Time Scales

Abstract

This paper is concerned with the existence and nonexistence of positive solutions of the p-Laplacian functional dynamic equation on a time scale, [ϕp(x▵(t))]∇+λa(t)f(x(t),x(u(t)))=0, t∈(0,T), x0(t)=ψ(t), t∈[−τ,0], x(0)−B0(x▵(0))=0, x▵(T)=0. We show that there exists a λ∗>0 such that the above boundary value problem has at least two, one, and no positive solutions for 0<λ<λ∗, λ=λ∗ and λ>λ∗, respectively.