Electron. J. Diff. Eqns., Vol. 2008(2008), No. 45, pp. 1-12.

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

Fuyi Xu, Zhenbo Chen, Feng Xu

Abstract:
In this paper, we study the nonlinear second-order m-point boundary value problem
$$\displaylines{
 u''(t)+f(t,u)=0,\quad  0\leq t \leq 1, \cr
 \beta u(0)-\gamma u'(0)=0,\quad
 u(1)=\sum _{i=1}^{m-2}\alpha_{i} u(\xi_{i}),
 }$$
where the nonlinear term $f$ is allowed to change sign. We impose growth conditions on $f$ which yield the existence of at least two positive solutions by using a fixed-point theorem in double cones. Moreover, the associated Green's function for the above problem is given.

Submitted December 27, 2007. Published March 29, 2008.
Math Subject Classifications: 34B15.
Key Words: m-point; boundary-value problem; Green's function; fixed point theorem in double cones.

Show me the PDF file (236 KB), TEX file, and other files for this article.

Fuyi Xu
School of Mathematics and Information Science
Shandong University of Technology
Zibo, Shandong, 255049, China
email: zbxufuyi@163.com
Zhenbo Chen
School of Mathematics and Information Science
Shandong University of Technology
Zibo, Shandong, 255049, China
email: czb56@sdut.edu.cn
Feng Xu
School of Mathematics and Information Science
Shandong University of Technology
Zibo, Shandong, 255049, China
email: zbxf878@126.com

Return to the EJDE web page