Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 34, pp. 1-8.
Title: Positive solutions for a nonlinear three-point boundary-value problem
Author: Ruyun Ma (Northwest Normal Univ. Gansu, China)
Abstract:
We study the existence of positive solutions to the boundary-value problem
$$ \displaylines
u''+a(t)f(u)=0,\quad t\in (0,1) \cr
u(0)=0,\quad\alpha u(\eta)=u(1)\,, \cr}
$$
where $0<\eta<1$ and $0<\alpha<1/\eta$.
We show the existence of at least one positive solution if $f$ is
either superlinear or sublinear by applying the fixed point theorem in cones.
Submitted June 9, 1999. Published September 15, 1999.
Math Subject Classifications: 34B15
Key Words: Second-order multi-point BVP; positive solution; cone; fixed point.