Existence of solutions for impulsive partial neutral functional differential equations

Hernández, M Eduardo; Rabello, Marco; Henrı́quez, Hernán R.

doi:10.1016/j.jmaa.2006.09.043

Cited by 150 publications

(85 citation statements)

References 33 publications

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“…In this section we discuss a partial differential equation applying the abstract results of this paper. In this application, B is the phase space 0 × 2 (ℎ, ) (see [10]). …”

Section: Examplesmentioning

confidence: 99%

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Existence of Solution and Approximate Controllability for Neutral Differential Equation with State Dependent Delay

Das

Pandey

Sukavanam

2014

International Journal of Partial Differential Equations

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This paper is divided in two parts. In the first part we study a second order neutral partial differential equation with state dependent delay and noninstantaneous impulses. The conditions for existence and uniqueness of the mild solution are investigated via Hausdorff measure of noncompactness and Darbo Sadovskii fixed point theorem. Thus we remove the need to assume the compactness assumption on the associated family of operators. The conditions for approximate controllability are investigated for the neutral second order system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. A simple range condition is used to prove approximate controllability. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in (Balachandran and Park, 2003), which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in (Dauer and Mahmudov, 2002), which are practically difficult to verify and apply. Examples are provided to illustrate the presented theory.

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“…In this section we discuss a partial differential equation applying the abstract results of this paper. In this application, B is the phase space 0 × 2 (ℎ, ) (see [10]). …”

Section: Examplesmentioning

confidence: 99%

“…For details see [7][8][9][10][11][12]. As a matter of fact, in these papers their authors assume severe conditions on the operator family generated by , which imply that the underlying space has finite dimension.…”

Section: Introductionmentioning

confidence: 99%

Existence of Solution and Approximate Controllability for Neutral Differential Equation with State Dependent Delay

Das

Pandey

Sukavanam

2014

International Journal of Partial Differential Equations

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“…The existence of almost periodic solutions for abstract impulsive dynamic equations was considered by many authors; see [10,16,24,25]. To the best of our knowledge, weighted piecewise pseudo double-almost periodic solutions for impulsive dynamic equations on ACCTS have never been considered in any literature.…”

Section: Introductionmentioning

confidence: 99%

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Wang¹,

Agarwal²,

O’Regan³

2017

J. Nonlinear Sci. Appl.

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In this paper, based on the concept and properties of almost-complete closedness time scales (ACCTS), we investigate the existence of weighted pseudo double-almost periodic mild solutions for non-autonomous impulsive evolution equations. We also consider the exponential stability of weighted pseudo double-almost periodic solutions. Finally, we conclude our paper by providing several illustrative applications to different types of dynamic equations and mathematical models. These applications justify the practical usefulness of the established theoretical results.

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“…Considerable work in the field of fixed impulsive type equations may be found in [9,16] and the references therein. The study of impulsive stochastic differential equations (ISDEs) is a new area of research and few publications on that subject can be found in the literature.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic stability of neutral stochastic functional integro-diﬀerential equations with impulses

Diop

Caraballo

2015

Electron. Commun. Probab.

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This paper is concerned with the existence and asymptotic stability in the p-th moment of mild solutions of nonlinear impulsive stochastic delay neutral partial functional integro-differential equations. We suppose that the linear part possesses a resolvent operator in the sense given in [8], and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is used to achieve the required result. An example is provided to illustrate the theory developed in this work. .

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Existence of solutions for impulsive partial neutral functional differential equations

Abstract: This paper is concerned with partial neutral functional differential equations of first and second order with impulses. We establish some results of existence of mild solutions for these classes of equations.

Cited by 150 publications

References 33 publications

Existence of Solution and Approximate Controllability for Neutral Differential Equation with State Dependent Delay

Existence of Solution and Approximate Controllability for Neutral Differential Equation with State Dependent Delay

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Asymptotic stability of neutral stochastic functional integro-diﬀerential equations with impulses

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