Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 151, pp. 1-7.
Title: Multiple positive solutions for second-order three-point
boundary-value problems with sign changing nonlinearities
Authors: Jian Liu (Shandong Univ. of Finance and Economics, China)
Zengqin Zhao (Qufu Normal Univ., Qufu, Shandong, China)
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 07, 2012.
Math Subject Classifications: 34B15, 34B25.
Key Words: Multiple positive solutions; sign changing; fixed-point theorem.