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

Abstract

In this paper, we study the singular semi-positone Neumann boundary-value problem -u'' + m2u = λƒ(t, u) + g(t, u), 0 < t < 1, u'(0) = u'(1) = 0, where m is a positive constant. Under some suitable assumptions on the functions ƒ and g, for sufficiently small λ, we prove the existence of a positive solution. Our approach is based on the Krasnasel'skii fixed point theorem in cones.