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

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• 作者：Yuji Liu ^{liuyuji888@sohu.com" class="auth_mail" title="E-mail the corresponding author yujiliu@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized Lane&ndash ; Emden system ; Four-point boundary value problem ; Positive solution ; Fixed point theorem
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：Complete
• 页码：200-225
• 全文大小：720 K

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 G(t,s)$G(t,s)$ for problem −(ρ(t)x^′(t))^′=0,lim_t→−∞x(t)−kx(ξ)=0,lim_t→+∞x(t)−lx(η)=0$-{\left(\rho \left(t\right)x^{\prime }\left(t\right)\right)}^{\prime }=0,{lim}_{t\to -\infty }x\left(t\right)-kx\left(\xi \right)=0,{lim}_{t\to +\infty }x\left(t\right)-lx\left(\eta \right)=0$, we prove that G(t,s)≥0$G(t,s)\ge 0$ 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.