Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory

In this paper, we investigate the existence of periodic solutions for a class of second order nonlinear random impulse differential equations. By extending the definitions of continuous function bound set, curvature bound set and Nagumo set in topological degree to PC space, and defining the appropr...

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Autores principales:	Lizhi Wang, Xiao-Bao Shu, Yilin Cheng, Ruijie Cui
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Random impulse differential equation Periodic solution Topological degree Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/698df00426444556a0994020f2bfe2e5
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spelling	oai:doaj.org-article:698df00426444556a0994020f2bfe2e52021-11-14T04:35:19ZExistence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory2590-037410.1016/j.rinam.2021.100215https://doaj.org/article/698df00426444556a0994020f2bfe2e52021-11-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2590037421000509https://doaj.org/toc/2590-0374In this paper, we investigate the existence of periodic solutions for a class of second order nonlinear random impulse differential equations. By extending the definitions of continuous function bound set, curvature bound set and Nagumo set in topological degree to PC space, and defining the appropriate operators and conditions, using the theory of topological degree and coincidence degree, we prove that the solution must be bounded if it exists and find the boundary value. Finally, we define appropriate Nagumo set and autonomous curvature bound set, and obtain the existence of periodic solutions of equations and simultaneous equations by using Mawhin’s continuity theorem.Lizhi WangXiao-Bao ShuYilin ChengRuijie CuiElsevierarticleRandom impulse differential equationPeriodic solutionTopological degreeMathematicsQA1-939ENResults in Applied Mathematics, Vol 12, Iss , Pp 100215- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Random impulse differential equation Periodic solution Topological degree Mathematics QA1-939
spellingShingle	Random impulse differential equation Periodic solution Topological degree Mathematics QA1-939 Lizhi Wang Xiao-Bao Shu Yilin Cheng Ruijie Cui Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory
description	In this paper, we investigate the existence of periodic solutions for a class of second order nonlinear random impulse differential equations. By extending the definitions of continuous function bound set, curvature bound set and Nagumo set in topological degree to PC space, and defining the appropriate operators and conditions, using the theory of topological degree and coincidence degree, we prove that the solution must be bounded if it exists and find the boundary value. Finally, we define appropriate Nagumo set and autonomous curvature bound set, and obtain the existence of periodic solutions of equations and simultaneous equations by using Mawhin’s continuity theorem.
format	article
author	Lizhi Wang Xiao-Bao Shu Yilin Cheng Ruijie Cui
author_facet	Lizhi Wang Xiao-Bao Shu Yilin Cheng Ruijie Cui
author_sort	Lizhi Wang
title	Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory
title_short	Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory
title_full	Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory
title_fullStr	Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory
title_full_unstemmed	Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory
title_sort	existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/698df00426444556a0994020f2bfe2e5
work_keys_str_mv	AT lizhiwang existenceofperiodicsolutionsofsecondordernonlinearrandomimpulsivedifferentialequationsviatopologicaldegreetheory AT xiaobaoshu existenceofperiodicsolutionsofsecondordernonlinearrandomimpulsivedifferentialequationsviatopologicaldegreetheory AT yilincheng existenceofperiodicsolutionsofsecondordernonlinearrandomimpulsivedifferentialequationsviatopologicaldegreetheory AT ruijiecui existenceofperiodicsolutionsofsecondordernonlinearrandomimpulsivedifferentialequationsviatopologicaldegreetheory
_version_	1718429901399261184

Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory

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