Existence of positive solutions of Neumann boundary value problem via a cone compression-expansion fixed point theorem of functional type

This paper is devoted to study the existence of positive solutions of second-order boundary value problem $$-u''+m^2u=h(t)f(t,u),\quad t\in (0,1)$$ with Neumann boundary conditions $$u'(0)=u'(1)=0,$$ where m>0, f∈C(0,1]×?⁺,?⁺), and h(t) is allowed to be singular at t=0 and t=1. The arguments are based only upon the positivity of the Green function, a fixed point theorem of cone expansion and compression of functional type, and growth conditions on the nonlinearity f.