Electron. J. Diff. Eqns., Vol. 2007(2007), No. 63, pp. 1-9.

Positive solutions for singular three-point boundary-value problems with sign changing nonlinearities depending on $x'$

Yun Chen, Baoqiang Yan, Lili Zhang

Abstract:
Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem
$$\displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,\quad 0 less than t less than 1,\cr x'(0)=0,\quad x(1)=\alpha x(\eta), }$$
where 0 less than $\alpha$ less than 1, 0 less than $\eta$ less than 1, and $f$ may change sign and may be singular at $x=0$ and $x'=0$.

Submitted September 15, 2006. Published April 25, 2007.
Math Subject Classifications: 34B15, 34B10.
Key Words: Three-point boundary value problem; singularity; positive solutions; fixed point theorem.

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Yun Chen
Department of Mathematics
Shandong Normal University
Jinan, 250014, China
email: chenyun001982@126.com
Baoqiang Yan
Department of Mathematics
Shandong Normal University
Jinan, 250014, China
email: yanbqcn@yahoo.com.cn
Lili Zhang
Department of Mathematics
Shandong Normal University
Jinan, 250014, China
email: kuaile100@163.com

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