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 ( x00.t/ 􀀀 k2.t/x.t/ C m.t/f .t; x.t// D 0; t 2 .0;1/; x.0/ D 0; lim t!1 x.t/ D 0; where k V T0;1/ ! .0;1/ and f V T0;1/ T0;1/ ! R are continuous. We show the existence of positive solutions by using a fixed point theorem in cones.