Advances in Difference Equations
Volume 2010 (2010), Article ID 809497, 15 pages
Research Article

Existence of Positive Solutions to a Nonlocal Boundary Value Problem with p-Laplacian onTime Scales

School of Mathematics and Information, Ludong University, Yantai, Shandong 264025, China

Received 6 October 2009; Accepted 19 January 2010

Academic Editor: Paul Eloe

Copyright © 2010 Ting-Ting Sun et al. 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.


The nonlocal boundary value problem, with p-Laplacian of the form (Φp(u))(t)+h(t)f(t,u(t))=0,  t[t1,tm)T,  u(t1)j=1nθju(ηj)i=1m2ϵiu(ξi)=0,  u(tm)=0, has been considered. Two existence criteria of at least one and three positive solutions are presented. The first one is based on the Four functionals fixed point theorem in the work of R. Avery et al. (2008), and the second one is based on the Five functionals fixed point theorem. Meanwhile an example is worked out to illustrate the main result.