Electron. J. Diff. Equ., Vol. 2012 (2012), No. 151, pp. 1-7.

Multiple positive solutions for second-order three-point boundary-value problems with sign changing nonlinearities

Jian Liu, Zengqin Zhao

Abstract:
In this article, we study the second-order three-point boundary-value problem
$$\displaylines{ u''(t)+a(t)u'(t)+f(t,u)=0,\quad 0 \leq t \leq 1, \cr u'(0)=0,\quad u(1)=\alpha u(\eta), }$$
where $0<\alpha$, $\eta<1$, $a\in C([0,1],(-\infty, 0))$ and $f$ is allowed to change sign. We show that there exist two positive solutions by using Leggett-Williams fixed-point theorem.

Submitted March 14, 2012. Published September 7, 2012.
Math Subject Classifications: 34B15, 34B25.
Key Words: Multiple positive solutions; sign changing; fixed-point theorem.

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Jian Liu
School of Mathematics and Quantitative Economics
Shandong University of Finance and Economics
Jinan, Shandong, 250014, China
email: liujianmath@163.com
Zengqin Zhao
School of Mathematical Sciences
Qufu Normal University, Qufu
Shandong, 273165, China
email: zqzhao@mail.qfnu.edu.cn

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