Advances in Difference Equations
Volume 2010 (2010), Article ID 809497, 15 pages
doi:10.1155/2010/809497

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

Ting-Ting Sun , Lin-Lin Wang and Yong-Hong Fan

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

Abstract

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.