Electron. J. Diff. Equ., Vol. 2012 (2012), No. 133, pp. 1-10.

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

Jingliang Qiu

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.

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Jingliang Qiu
School of Applied Science
Beijing InformationScience and Technology University
Beijing, 100192, China
email: jingliangqiu@sina.cn   Tel: +86-010-82426111

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