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