Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 133, pp. 1-10.

Title: Positive solutions for a nonlinear periodic
       boundary-value problem with a parameter

Author: Jingliang Qiu (Beijing Information Science and  Tech. Univ, China)

Abstract:
 Using topological degree theory with a partially ordered structure 
 of space,  sufficient conditions for the existence and multiplicity of
 positive solutions for a second-order nonlinear periodic
 boundary-value problem are established.
 Inspired by ideas in Guo and Lakshmikantham [6], we study
 the dependence of positive periodic solutions as a parameter
 approaches infinity,
 $$
 \lim_{\lambda\to +\infty}\|x_{\lambda}\|=+\infty,\quad\hbox{or}\quad
 \lim_{\lambda\to+\infty}\|x_{\lambda}\|=0.
 $$

Submitted May 22, 2012. Published August 17, 2012.
Math Subject Classifications: 34B18, 34B15.
Key Words: Periodic boundary value problem;  fixed point;
           partially ordered structure; positive solutions.