Multiple positive solutions of multi-point boundary value problems on the half-line

Abstract

In this paper, we investigate the existence of positive solutions for multi-point boundary value problems on the half-line. Under various weaker conditions, we establish various results on the existence of multiple positive solutions for multi-point boundary value problems on the half-line by applying the fixed-point theorem of cone expansion and compression type due to Krasnosel’skill in a special function space. Especially, we allow the nonlinear terms to have suitable singularities. Our results significantly extend and improve many known results even for nonsingular cases.