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

Abstract

In this paper, we consider the boundary value problem on the half-line { x ″ ( t ) − k 2 ( t ) x ( t ) + λ m ( t ) f ( t , x ( t ) ) = 0 , t ∈ ( 0 , ∞ ) , x ( 0 ) = 0 , lim t → ∞ x ( t ) = 0 , where k : [ 0 , ∞ ) → ( 0 , ∞ ) and f : [ 0 , ∞ ) × [ 0 , ∞ ) → R are continuous. We show the existence of positive solutions by using a fixed point theorem in cones.