Advances in Difference Equations
Volume 2008 (2008), Article ID 879140, 9 pages
doi:10.1155/2008/879140
Research Article
Eigenvalue Problems for p-Laplacian Functional Dynamic Equations on Time Scales
School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China
Received 29 February 2008; Accepted 25 June 2008
Academic Editor: Johnny Henderson
Copyright © 2008 Changxiu Song. 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
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.