文摘
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 ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300566&_mathId=si1.gif&_user=111111111&_pii=S1468121816300566&_rdoc=1&_issn=14681218&md5=058bb4ab69d5e190a4a5f2b4c2c28acc" title="Click to view the MathML source">G(t,s)er hidden">e"> for problem ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300566&_mathId=si2.gif&_user=111111111&_pii=S1468121816300566&_rdoc=1&_issn=14681218&md5=34bcc4211dabaa755a7efacfab47c29f" title="Click to view the MathML source">−(ρ(t)x′(t))′=0,limt→−∞x(t)−kx(ξ)=0,limt→+∞x(t)−lx(η)=0er hidden">e">, we prove that ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300566&_mathId=si3.gif&_user=111111111&_pii=S1468121816300566&_rdoc=1&_issn=14681218&md5=fe6e909c5c7ee97c81a1cb8d1f17fc9c" title="Click to view the MathML source">G(t,s)≥0er hidden">e"> 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.