The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems

Abstract In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville differential equation with random impulses. Then, we get the equivalent integral eq...

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Autores principales:	Zihan Li, Xiao-Bao Shu, Tengyuan Miao
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Random impulsive differential equation Green function Upper and lower solution Fixed point theorem Boundary value problems Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/32670bb8713741a3a8aaaabfab23d3ff
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spelling	oai:doaj.org-article:32670bb8713741a3a8aaaabfab23d3ff2021-11-28T12:08:55ZThe existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems10.1186/s13661-021-01574-x1687-2770https://doaj.org/article/32670bb8713741a3a8aaaabfab23d3ff2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13661-021-01574-xhttps://doaj.org/toc/1687-2770Abstract In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville differential equation with random impulses. Then, we get the equivalent integral equation of the random impulsive differential equation. Based on this integral equation, we use Dhage’s fixed point theorem to prove the existence of solutions to the equation, and the theorem is extended to the general second order nonlinear random impulsive differential equations. Then we use the upper and lower solution method to give a monotonic iterative sequence of the generalized random impulsive Sturm–Liouville differential equations and prove that it is convergent. Finally, we give two concrete examples to verify the correctness of the results.Zihan LiXiao-Bao ShuTengyuan MiaoSpringerOpenarticleRandom impulsive differential equationGreen functionUpper and lower solutionFixed point theoremBoundary value problemsAnalysisQA299.6-433ENBoundary Value Problems, Vol 2021, Iss 1, Pp 1-23 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Random impulsive differential equation Green function Upper and lower solution Fixed point theorem Boundary value problems Analysis QA299.6-433
spellingShingle	Random impulsive differential equation Green function Upper and lower solution Fixed point theorem Boundary value problems Analysis QA299.6-433 Zihan Li Xiao-Bao Shu Tengyuan Miao The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems
description	Abstract In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville differential equation with random impulses. Then, we get the equivalent integral equation of the random impulsive differential equation. Based on this integral equation, we use Dhage’s fixed point theorem to prove the existence of solutions to the equation, and the theorem is extended to the general second order nonlinear random impulsive differential equations. Then we use the upper and lower solution method to give a monotonic iterative sequence of the generalized random impulsive Sturm–Liouville differential equations and prove that it is convergent. Finally, we give two concrete examples to verify the correctness of the results.
format	article
author	Zihan Li Xiao-Bao Shu Tengyuan Miao
author_facet	Zihan Li Xiao-Bao Shu Tengyuan Miao
author_sort	Zihan Li
title	The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems
title_short	The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems
title_full	The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems
title_fullStr	The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems
title_full_unstemmed	The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems
title_sort	existence of solutions for sturm–liouville differential equation with random impulses and boundary value problems
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/32670bb8713741a3a8aaaabfab23d3ff
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The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems

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