Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 111, pp. 1-11.
Title: Positive solutions for an m-point boundary-value problem
Authors: Le Xuan Truong (Univ. of Technical Education, HoChiMinh, Vietnam)
Le Thi Phuong Ngoc (Nhatrang Educational College, Vietnam)
Nguyen Thanh Long (Vietnam National University HoChiMinh, Vietnam)
Abstract:
In this paper, we obtain sufficient conditions for the existence of
a positive solution, and infinitely many positive solutions, of the
m-point boundary-value problem
$$\displaylines{
x''(t) = f(t, x(t)), \quad 0 < t < 1, \cr
x'(0) = 0, \quad x(1)=\sum_{i=1}^{m-2}\alpha _{i}x(\eta _{i})\,.
}$$
Our main tools are the Guo-Krasnoselskii's fixed point theorem
and the monotone iterative technique.
We also show that the set of positive solutions is compact.
Submitted April 22, 2008. Published August 15, 2008.
Math Subject Classifications: 34B07, 34B10, 34B18, 34B27.
Key Words: Multi-point boundary; positive solution;
Guo-Krasnoselskii fixed point theorem.