Electron. J. Diff. Eqns., Vol. 2008(2008), No. 147, pp. 1-29.

Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivative

Ya Ma, Baoqiang Yan

Abstract:
Using the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular $m$-point boundary-value problem
$$\displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,\quad 0<t<1,\cr x'(0)=0,\quad x(1)= \sum_{i=1}^{m-2}a_{i}x(\xi_i), }$$
where $0<\xi_1<\xi_2<\dots<\xi_{m-2}<1$, $a_i\in [0,1)$, $i = 1, 2,\dots, m-2$, with $0< \sum_{i=1}^{m-2}a_i <1 $ and $f$ maybe singular at $x=0$ and $x'=0$.

Submitted August 13, 2008. Published October 24, 2008.
Math Subject Classifications: 34B10, 34B15.
Key Words: m-point boundary-value problem; singularity; positive solutions; fixed point theorem.

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Ya Ma
Department of Mathematics
Shandong Normal University
Jinan, 250014, China
email: maya-0907@163.com
Baoqiang Yan
Department of Mathematics
Shandong Normal University
Jinan, 250014, China
mail: yanbqcn@yahoo.com.cn

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