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

This paper is concerned with four-point boundary value problem of second order singular differential equtions on whole line. Green’s function G(t, s) for problem (Formula presented) is obtained. We proved that G(t, s) ≥ 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. © Korean Society for Computational and Applied Mathematics 2015.