Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 96, pp. 1-10.

Title: Existence, multiplicity and infinite solvability of positive
       solutions for $p$-Laplacian dynamic equations on time scales

Author: Da-Bin Wang (Lanzhou Univ. of Technology, China)

Abstract: 
 In this paper, by using Guo-Krasnosel'skii fixed point theorem in cones,
 we study the existence, multiplicity and infinite solvability of positive
 solutions for the following three-point boundary value problems for
 $p$-Laplacian dynamic equations on time scales
 $$\displaylines{
 [ \Phi _p(u^{\triangle }(t))] ^{\triangledown}+a(t)f(t,u(t))
 =0,\quad t\in [0,T]_{\mathbf{T}}, \cr
 u(0)-B_0(u^{\triangle }(\eta )) = 0,\quad u^{\triangle }(T)=0.
 }$$
 By multiplicity we mean the existence of arbitrary number of solutions.

Submitted April 14, 2006. Published August 22, 2006.
Math Subject Classifications: 34B10, 34B18, 39A10.
Key Words: Time scales; $p$-Laplacian; boundary value problem;
 positive solution; existence; multiplicity; infinite solvability.