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.