This paper is concerned with four-point boundary value problems of the one-dimensional generalized Lane-Emden systems on whole lines. The Green’s functions G(t, s) for the problem −(ρ(t)x′(t))′ = 0 with boundary conditions
are obtained respectively. We proved that G(t, s) ≥ 0 under some assumptions which actually generalize a corresponding result in [J. Math. Anal. Appl. 305 (2005) 253-276]. Sufficient conditions to guarantee the existence of positive solutions of this kind of models are established. Examples are given at the end of the paper.
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