Existence of positive solutions of four-point BVPs for singular generalized Lane–Emden systems on whole line

Abstract

In this paper, we firstly introduce a model of four-point boundary value problem for generalized singular Lane–Emden systems on whole line. By establishing Green’s function G(t,s) for problem −(ρ(t)x′(t))′=0,limt→−∞x(t)−kx(ξ)=0,limt→+∞x(t)−lx(η)=0, we prove that G(t,s)≥0 under some assumptions which actually generalize a corresponding result in Liu (2004). We then obtain sufficient conditions to guarantee existence of positive solutions of this kind of models. Finally, three examples are given at the end of the paper to illustrate main theorems.