Existence of positive solutions for a semipositone boundary value problem on the half-line

In this paper, we consider the boundary value problem on the half-line {x″(t)−k2(t)x(t)+λm(t)f(t,x(t))=0,t∈(0,∞),x(0)=0,limt→∞x(t)=0, where k:[0,∞)→(0,∞)k:[0,∞)→(0,∞) and f:[0,∞)×[0,∞)→Rf:[0,∞)×[0,∞)→R are continuous. We show the existence of positive solutions by using a fixed point theorem in cones.