Advances in Difference Equations
Volume 2008 (2008), Article ID 879140, 9 pages
Research Article

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

Changxiu Song

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.


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.