Analysis on Existence of Positive Solutions for a Class Second Order Semipositone Differential Equations

Abstract

In this paper, we study the existence of positive solutions of the following second-order semipositone system −u″+ρu=ϕu+ft,u,ϕ,t∈0,1,−ϕ″=μu,t∈0,1,u0=u1=ϕ0=ϕ1=0.. By applying a well-known fixed-point theorem, we prove that the problem admits at least one positive solution, if f is bounded below.