Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 133, pp. 1-8.

Title: Positive solutions for singular semi-positone  Neumann
       boundary-value problems

Authors: Yong-Ping Sun (Qufu Normal Univ., China)
         Yan Sun (Qufu Normal Univ., China)

Abstract: 
 In  this paper, we study the singular semi-positone Neumann 
 bound\-ary-value problem
 $$\displaylines{
  -u''+m^2u=\lambda f(t,u)+g(t,u),\quad 0<t<1,\cr
  u'(0)=u'(1)=0,
 }$$
 where $m$ is a positive constant.
 Under some suitable assumptions on the functions $f$ and $g$,
 for sufficiently small $\lambda$, we prove the existence of a
 positive solution. Our approach is based on the Krasnasel'skii
 fixed point theorem in cones.

Submitted October 12, 2004. Published November 16, 2004.
Math Subject Classifications: 34B10, 34B15.
Key Words: Positive solution; semi-positone; fixed points; cone; 
singular Neumann boundary-value problem.