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.