Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs

We are concerned with the following system of third-order three-point boundary value problems: u′′′(t)+f(t,v(t))=0, t∈(0,1), v′′′(t)+g(t,u(t))=0, t∈(0,1), u(0)=u′′(0)=0, u′(1)=αu(η), v(0)=v′′(0)=0, and v′(1)=αv(η), where 0<η<1 and 0<α<1/η. By imposing some suitable conditions on f and g,...

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Main Authors:	Jian-Ping Sun, Xue-Mei Yang, Ya-Hong Zhao
Format:	Article
Language:	English
Published:	Hindawi Limited 2016-01-01
Series:	Journal of Function Spaces
Online Access:	http://dx.doi.org/10.1155/2016/6874643

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spelling	doaj-f58ad81e246747b08d05babb88d491022020-11-24T21:46:33ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/68746436874643Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPsJian-Ping Sun0Xue-Mei Yang1Ya-Hong Zhao2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaWe are concerned with the following system of third-order three-point boundary value problems: u′′′(t)+f(t,v(t))=0, t∈(0,1), v′′′(t)+g(t,u(t))=0, t∈(0,1), u(0)=u′′(0)=0, u′(1)=αu(η), v(0)=v′′(0)=0, and v′(1)=αv(η), where 0<η<1 and 0<α<1/η. By imposing some suitable conditions on f and g, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.http://dx.doi.org/10.1155/2016/6874643
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jian-Ping Sun Xue-Mei Yang Ya-Hong Zhao
spellingShingle	Jian-Ping Sun Xue-Mei Yang Ya-Hong Zhao Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs Journal of Function Spaces
author_facet	Jian-Ping Sun Xue-Mei Yang Ya-Hong Zhao
author_sort	Jian-Ping Sun
title	Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs
title_short	Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs
title_full	Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs
title_fullStr	Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs
title_full_unstemmed	Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs
title_sort	existence of positive solution to system of nonlinear third-order three-point bvps
publisher	Hindawi Limited
series	Journal of Function Spaces
issn	2314-8896 2314-8888
publishDate	2016-01-01
description	We are concerned with the following system of third-order three-point boundary value problems: u′′′(t)+f(t,v(t))=0, t∈(0,1), v′′′(t)+g(t,u(t))=0, t∈(0,1), u(0)=u′′(0)=0, u′(1)=αu(η), v(0)=v′′(0)=0, and v′(1)=αv(η), where 0<η<1 and 0<α<1/η. By imposing some suitable conditions on f and g, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.
url	http://dx.doi.org/10.1155/2016/6874643
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Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs

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