Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 95, pp. 1-9.
Title: Three positive solutions for p-Laplacian functional dynamic
equations on time scales
Author: Da-Bin Wang (Lanzhou Univ., Gansu, China)
Abstract:
In this paper, we establish the existence of three positive solutions
to the following p-Laplacian functional dynamic equation on time scales,
$$\displaylines{
[ \Phi _p(u^{\Delta }(t))] ^{\nabla}+a(t)f(u(t),u(\mu (t)))=0,\quad
t\in (0,T)_{\mathbf{T}}, \cr
u_0(t)=\varphi (t),\quad t\in [-r,0] _{\mathbf{T}},\\
u(0)-B_0(u^{\Delta }(\eta ))=0,\quad u^{\Delta }(T)=0,.
}$$
using the fixed-point theorem due to Avery and Peterson [8].
An example is given to illustrate the main result.
Submitted May 17, 2007. Published June 29, 2007.
Math Subject Classifications: 39A10, 34B15.
Key Words: Time scale; p-Laplacian functional dynamic equation;
boundary value problem; positive solution; fixed point.