Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 65, pp. 1-8.
Title: Positive solutions to a second order multi-point boundary-value problem
Authors: Daomin Cao (Institute of Applied Math., Beijing, China)
Ruyun Ma (Northwest Normal Univ. Gansu, China)
Abstract:
We prove the existence of positive solutions to the boundary-value problem
$$ \displaylines{
u''+\lambda a(t)f(u,u')=0 \cr
u(0)=0,\quad u(1)=\sum^{m-2}_{i=1} a_i u(\xi_i) \,,
}$$
where $a$ is a continuous function that may change sign on $[0,1]$,
$f$ is a continuous function with $f(0,0)>0$, and $\lambda$ is a samll
positive constant. For finding solutions we use the Leray-Schauder
fixed point theorem.
Submitted September 18, 2000. Published October 30, 2000.
Math Subject Classifications: 34B10.
Key Words: Multi-point boundary value problem; positive solution;
fixed point theorem.