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December 2015 Existence of positive solutions of four-point BVPs for one-dimensional generalized Lane-Emden systems on whole line
Pinghua Yang, Yuji Liu
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Tbilisi Math. J. 8(2): 257-280 (December 2015). DOI: 10.1515/tmj-2015-0026

Abstract

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 $-(\rho(t)x'(t))'=0$ with boundary conditions $\lim\limits_{t\to-\infty}x(t)-kx(\xi)= \lim\limits_{t\to +\infty}x(t)-l x(\eta)=0$ and $\lim\limits_{t\to-\infty}x(t)-kx(\xi)= \lim\limits_{t\to +\infty}\rho(t)x'(t)-l \rho(\eta)x'(\eta)=0$ are obtained respectively. We proved that $G(t,s)\ge 0$ 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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Pinghua Yang. Yuji Liu. "Existence of positive solutions of four-point BVPs for one-dimensional generalized Lane-Emden systems on whole line." Tbilisi Math. J. 8 (2) 257 - 280, December 2015. https://doi.org/10.1515/tmj-2015-0026

Information

Received: 18 November 2014; Accepted: 21 October 2015; Published: December 2015
First available in Project Euclid: 12 June 2018

zbMATH: 1336.34043
MathSciNet: MR3441141
Digital Object Identifier: 10.1515/tmj-2015-0026

Subjects:
Primary: 34B10
Secondary: 34B15, 35B10

Rights: Copyright © 2015 Tbilisi Centre for Mathematical Sciences

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Vol.8 • No. 2 • December 2015
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