Research of the three-point boundary value problems for nonlinear second-order difference equation

In order to extend the basic theory of nonlinear discrete boundary value problems,this paper studied the sufficient conditions for the existence of positive solutions for a class of nonlinear second-order difference equations with three-point boundary value problems.Firstly,the expressions of the so...

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Autores principales:	Wenying WEI, Yude JI, Yanping GUO
Formato:	article
Lenguaje:	ZH
Publicado:	Hebei University of Science and Technology 2021
Materias:	difference equation; discrete boundary value problem; fixed point theorem; cone; positive solution; existence Technology T
Acceso en línea:	https://doaj.org/article/c9cce54491b64a05baa9694ead6056b0
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spelling	oai:doaj.org-article:c9cce54491b64a05baa9694ead6056b02021-11-23T07:08:58ZResearch of the three-point boundary value problems for nonlinear second-order difference equation1008-154210.7535/hbkd.2021yx04006https://doaj.org/article/c9cce54491b64a05baa9694ead6056b02021-08-01T00:00:00Zhttp://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b202104006&flag=1&journal_https://doaj.org/toc/1008-1542In order to extend the basic theory of nonlinear discrete boundary value problems,this paper studied the sufficient conditions for the existence of positive solutions for a class of nonlinear second-order difference equations with three-point boundary value problems.Firstly,the expressions of the solutions for the corresponding three-point boundary value problems for second-order difference equations were given and their properties were proved; Secondly,by constructing suitable cone and integral operator in Banach space and utilizing Krasnoselskii's fixed point theorem in cones,the sufficient conditions for the existence of positive solutions of three-point boundary value problems for nonlinear second-order difference equations were obtained under the condition that the nonlinear term was allowed to change sign.Finally,two examples were given to illustrate the validity of the main theorems and results.The results show that the conditions of the theorem are proved and the discrete boundary value problems satisfies the existence condition of positive solutions.The method is effective in the theoretical proof of the second-order discrete boundary value problem,and has reference for the study of the nonlinear high-order multi-point discrete boundary value problems.Wenying WEIYude JIYanping GUOHebei University of Science and Technologyarticledifference equation; discrete boundary value problem; fixed point theorem; cone; positive solution; existenceTechnologyTZHJournal of Hebei University of Science and Technology, Vol 42, Iss 4, Pp 360-368 (2021)
institution	DOAJ
collection	DOAJ
language	ZH
topic	difference equation; discrete boundary value problem; fixed point theorem; cone; positive solution; existence Technology T
spellingShingle	difference equation; discrete boundary value problem; fixed point theorem; cone; positive solution; existence Technology T Wenying WEI Yude JI Yanping GUO Research of the three-point boundary value problems for nonlinear second-order difference equation
description	In order to extend the basic theory of nonlinear discrete boundary value problems,this paper studied the sufficient conditions for the existence of positive solutions for a class of nonlinear second-order difference equations with three-point boundary value problems.Firstly,the expressions of the solutions for the corresponding three-point boundary value problems for second-order difference equations were given and their properties were proved; Secondly,by constructing suitable cone and integral operator in Banach space and utilizing Krasnoselskii's fixed point theorem in cones,the sufficient conditions for the existence of positive solutions of three-point boundary value problems for nonlinear second-order difference equations were obtained under the condition that the nonlinear term was allowed to change sign.Finally,two examples were given to illustrate the validity of the main theorems and results.The results show that the conditions of the theorem are proved and the discrete boundary value problems satisfies the existence condition of positive solutions.The method is effective in the theoretical proof of the second-order discrete boundary value problem,and has reference for the study of the nonlinear high-order multi-point discrete boundary value problems.
format	article
author	Wenying WEI Yude JI Yanping GUO
author_facet	Wenying WEI Yude JI Yanping GUO
author_sort	Wenying WEI
title	Research of the three-point boundary value problems for nonlinear second-order difference equation
title_short	Research of the three-point boundary value problems for nonlinear second-order difference equation
title_full	Research of the three-point boundary value problems for nonlinear second-order difference equation
title_fullStr	Research of the three-point boundary value problems for nonlinear second-order difference equation
title_full_unstemmed	Research of the three-point boundary value problems for nonlinear second-order difference equation
title_sort	research of the three-point boundary value problems for nonlinear second-order difference equation
publisher	Hebei University of Science and Technology
publishDate	2021
url	https://doaj.org/article/c9cce54491b64a05baa9694ead6056b0
work_keys_str_mv	AT wenyingwei researchofthethreepointboundaryvalueproblemsfornonlinearsecondorderdifferenceequation AT yudeji researchofthethreepointboundaryvalueproblemsfornonlinearsecondorderdifferenceequation AT yanpingguo researchofthethreepointboundaryvalueproblemsfornonlinearsecondorderdifferenceequation
_version_	1718416850159665152

Research of the three-point boundary value problems for nonlinear second-order difference equation

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