Existence of positive solutions for Sturm–Liouville boundary value problems on the half-line

In this paper, we establish sufficient conditions to guarantee the existence of at least one positive solution, a unique positive solution, and multiple positive solutions for the Sturm–Liouville boundary value problem on the half-line. By using an effective operator, the fixed point theorems in cone, especially Krasnoselskii fixed point theorem, can be applied to such systems and then existence criteria are established. The interesting point of the results is that the nonlinear term f can be sign-changing.