Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 45, pp. 1-12.
Title: Multiple positive solutions for nonlinear second-order m-point
boundary-value problems with sign changing nonlinearities
Authors: Fuyi Xu (Shandong Univ. of Technology, China)
Zhenbo Chen (Shandong Univ. of Technology, China)
Feng Xu (Shandong Univ. of Technology, China)
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.