Existence of Positive Solutions of Neumann Boundary Value Problem via a Convex Functional Compression-Expansion Fixed Point Theorem

摘要

This paper is devoted to study the existence of positive solutions of second-order bound-ary value problem?u 00 + Mu = h(t)f(t,u), t ∈ (0,1)with Neumann boundary conditionsu 0 (0) = u 0 (1) = 0,where M > 0, f ∈ C([0,1] × R + ,R + ). h(t) is allowed to be singular at t = 0 and t = 1. Thearguments are based only upon the positivity of the Green’s function and the fixed point theorem ofcone expansion and compression of convex function type.