Existence and non-existence of positive solutions of four-point BVPs for ODEs on whole line

Abstract

This paper is concerned with four-point boundary value problem of second order singular differential equations on whole line. Green's functions) ≥ 0 under some assumptions which actually generalize a corresponding result in Liu (Appl Math Comput 155(1):179-203, 2004) (see Remark 2.1). Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. We give two examples and remarks to illustrate main theorems.