Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 95, pp. 1-11.

Title: Multiple symmetric positive solutions to four-point 
       boundary-value problems of differential systems with p-Laplacian

Authors: Hanying Feng (Shijiazhuang Mechanical Engineering College. China)
         Donglong Bai (Shijiazhuang Mechanical Engineering College. China)
	 Meiqiang Feng (Beijing Information Science and Tech. Univ., China)

Abstract:
 In this article,  we study the four-point boundary-value problem
 with the one-dimensional p-Laplacian
 $$\displaylines{
 (\phi_{p_i}(u_i'))'+q_i(t)f_i(t,u_1,u_2)=0,\quad
 t\in(0,1),\quad i=1,2;\cr
 u_i(0)-g_i(u_i'(\xi))=0,\quad
 u_i(1)+g_i(u_i'(\eta))=0, \quad i=1,2.
 }$$
 We obtain sufficient conditions such that by means of a fixed point
 theorem on a cone,  there exist  multiple  symmetric positive solutions
 to the above boundary-value problem. As an application, we give an example
 that we illustrates  our results.

Submitted March 9, 2012. Published June 10, 2012.
Math Subject Classifications: 34B10, 34B15, 34B18.
Key Words: Four-point boundary-value problem; differential system;
           fixed point theorem; symmetric positive solution;
           one-dimensional p-Laplacian