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.

Show me the PDF file (204 KB), TEX file, and other files for this article.

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

Return to the EJDE web page