Existence and stability of almost periodic solutions for impulsive differential equations

Liu, Junwei; Zhang, Chuanyi

doi:10.1186/1687-1847-2012-34

Cited by 11 publications

(7 citation statements)

References 26 publications

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“…For more details about this topic, one can see [6,7,9,16,23,24,26], where the authors have given an important overview about the theory of impulsive differential and integro-differential equations. On the other hand, the asymptotic properties of solutions of impulsive differential equations have been studied from different points, such as almost periodicity [8,17,18,20,21,29], almost automorphy [1,30], asymptotic stability [19,28], asymptotic equivalence [5], and oscillation [15]. However, the existence and uniqueness of a piecewise asymptotically almost periodic mild solution for neutral Volterra integro-differential equations with impulsive effects in the form (1.1) is an untreated topic in the literature and this fact is the motivation of the present work.…”

Section: ) Where A(t) : D ⊂ X → X Are a Family Of Closed Linear Opermentioning

confidence: 99%

Piecewise asymptotically almost periodic solution ofneutral Volterra integro-differential equations with impulsiveeffects

Xia¹

2017

Turk J Math

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In this paper, we investigate the existence and uniqueness of a piecewise asymptotically almost periodic mild solution to nonautonomous neutral Volterra integro-differential equations with impulsive effects in Banach space. The working tools are based on the Krasnoselskii's fixed point theorem and semigroup theory. In order to illustrate our main results, we study the piecewise asymptotically almost periodic solution of the impulsive partial differential equations with Dirichlet conditions.

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Section: ) Where A(t) : D ⊂ X → X Are a Family Of Closed Linear Opermentioning

confidence: 99%

Piecewise asymptotically almost periodic solution ofneutral Volterra integro-differential equations with impulsiveeffects

Xia¹

2017

Turk J Math

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“…Lemma 2.10 and Lemma 2.11 are stochastic generalized versions of Lemma 4.1 in [12] and Lemma 35 in [23], respectively, and one may refer to [23,18,19,26,2,13,12] for more details. Here we omit the proofs.…”

Section: Preliminariesmentioning

confidence: 99%

“…There has been a significant development in the theory of impulsive differential equations. For example, the existence of almost periodic (mild) solutions of abstract impulsive differential equations have been considered in [23,24,25,4,18,19].…”

Section: Introductionmentioning

confidence: 99%

Existence and Stability of Almost Periodic Solutions to Impulsive Stochastic Differential Equations

Liu

Zhang

2013

Cubo

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This paper introduces the concept of square-mean piecewise almost periodic for impulsive stochastic processes. The existence of square-mean piecewise almost periodic solutions for linear and nonlinear impulsive stochastic differential equations is established by using the theory of the semigroups of the operators and Schauder fixed point theorem. The stability of the square-mean piecewise almost periodic solutions for nonlinear impulsive stochastic differential equations is investigated. RESUMEN Este artículo introduce el concepto de periodicidad cuadrática media por tramos casi periódica para procesos estocásticos impulsivos. La existencia de soluciones de media cuadrática casi periódicas para ecuaciones diferenciales estocásticas impulsivas lineales y no lineales se establece usando la teoría de semigrupos de los operadores y el teorema de punto fijo de Schauder. Se estudia la estabilidad de las soluciones de media cuadrática por tramos casi periódica para ecuaciones diferenciales estocásticas impulsivas no lineales.

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“…The almost periodic properties also have an important value in impulsive differential systems, and the analysis of the impulsive effects on the almost periodic behavior of solutions to such integer [38][39][40][41][42] and fractional-order [43][44][45][46][47] systems has received significant attention. Therefore, their effects on the almost periodic behavior of fractional-order inclusions should be further investigated.…”

Section: Introductionmentioning

confidence: 99%

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

Stamov

Stamova

2021

Mathematics

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In the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of operator semigroups, Hausdorff measure of noncompactness, fixed point theorems and fractional calculus techniques. Applications to a class of fractional-order impulsive gene regulatory network (GRN) models are proposed to illustrate the results.

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Existence and stability of almost periodic solutions for impulsive differential equations

Abstract: In this article, by using Schauder's fixed point theorem, we study the existence of almost periodic solutions for abstract impulsive differential equations. In addition, sufficient conditions for their asymptotic stability are obtained by means of generalized Gronwall-Bellman inequality.

Cited by 11 publications

References 26 publications

Piecewise asymptotically almost periodic solution ofneutral Volterra integro-differential equations with impulsiveeffects

Piecewise asymptotically almost periodic solution ofneutral Volterra integro-differential equations with impulsiveeffects

Existence and Stability of Almost Periodic Solutions to Impulsive Stochastic Differential Equations

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

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