Positive solutions for singular semi-positone Neumann boundary-value problems - Yong-Ping Sun (Electronic Journal of Differential Equations, 2004)
In this paper, we study the singular semi-positone Neumann bound-ary-value problem $$displaylines{ -u''+m^2u=lambda f(t,u)+g(t,u),quad 0 less than t less than 1,cr u'(0)=u'(1)=0, }$$ 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.