scholarly journals Existence for a Second-Order Impulsive Neutral Stochastic Integrodifferential Equations with Nonlocal Conditions and Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Dang Huan Diem
Keyword(s):  
Infinite Delay ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Linear Operators ◽  
Bounded Linear ◽  
Infinite Delays ◽  
Strongly Continuous Cosine Family

The current paper is concerned with the existence of mild solutions for a class of second-order impulsive neutral stochastic integrodifferential equations with nonlocal conditions and infinite delays in a Hilbert space. A sufficient condition for the existence results is obtained by using the Krasnoselskii-Schaefer-type fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. Finally, an application to the stochastic nonlinear wave equation with infinite delay is given.

scholarly journals Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces

2004 ◽  
Vol 2004 (22) ◽  
pp. 1133-1149
Author(s):  
S. Marshal Anthoni ◽  
J.-H. Kim ◽  
J. P. Dauer
Keyword(s):  
Banach Spaces ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Functional Differential ◽  
Functional Differential Inclusions ◽  
Condensing Maps

We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.

scholarly journals Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Meili Li ◽  
Chunhai Kou
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fractional Power Of Operators

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.

Exact and trajectory controllability of second order nonlinear differential equations with deviated argument

2017 ◽  
Vol 26 (2) ◽  
pp. 181-191
Author(s):  
M. MUSLIM ◽  
AVADHESH KUMAR ◽  
RAVI P. AGARWAL
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Exact Controllability ◽  
Second Order ◽  
Fixed Point Method ◽  
Linear Operators ◽  
Cosine Family ◽  
Bounded Linear ◽  
Deviated Argument ◽  
Strongly Continuous Cosine Family

In this manuscript, we consider a control system governed by a second order nonlinear differential equations with deviated argument in a Hilbert space X. We used the strongly continuous cosine family of bounded linear operators and fixed point method to study the exact and trajectory controllability. Also, we study the exact controllability of the nonlocal control problem. Finally, we give an example to illustrate the application of these results.

scholarly journals On Approximate Controllability of Second-Order Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects

2015 ◽  
Vol 2015 ◽  
pp. 1-26 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Stochastic Analysis ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Approximation Techniques ◽  
Approximately Controllable ◽  
Stochastic Functional

We discuss the approximate controllability of second-order impulsive neutral partial stochastic functional integrodifferential inclusions with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using the fixed point strategy, stochastic analysis, and properties of the cosine family of bounded linear operators combined with approximation techniques, a new set of sufficient conditions for approximate controllability of the second-order impulsive partial stochastic integrodifferential systems are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.

scholarly journals Existence of Second Order Impulsive Neutral Integro-Differential Evolution Control Systems with an Infinite Delay

2019 ◽  
Vol 8 (3) ◽  
pp. 8857-8862
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Evolution Control ◽  
Evolution Systems

This article, we study sufficient conditions for the controllability of second-order impulsive neutral integrodifferential evolution systems with an infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

scholarly journals A Study of Second Order Impulsive Neutral Evolution Differential Control Systems with an Infinite Delay

2018 ◽  
Author(s):  
P. Palani ◽  
T. Gunasekar ◽  
M. Angayarkanni ◽  
D. Kesavan
Keyword(s):  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Neutral Evolution ◽  
Differential Systems ◽  
Bounded Linear ◽  
Cosine Families ◽  
Differential Control

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

Asymptotic behavior of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2727-2748
Author(s):  
Zuomao Yan ◽  
Xiumei Jia
Keyword(s):  
Asymptotic Behavior ◽  
Hilbert Spaces ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Lipschitz Continuous ◽  
Stochastic Functional

In this paper, the existence and asymptotic stability in p-th moment of mild solutions to a class of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay in Hilbert spaces is considered. By using H?lder?s inequality, stochastic analysis, fixed point strategy and the theory of strongly continuous cosine families with the Hausdorff measure of noncompactness, a new set of sufficient conditions is formulated which guarantees the asymptotic behavior of the nonlinear second-order stochastic system. These conditions do not require the nonlinear terms are assumed to be Lipschitz continuous. An example is also discussed to illustrate the efficiency of the obtained results.

scholarly journals A Study of Second Order Impulsive Neutral Evolution Control Systems with an Infinite Delay

2018 ◽  
Author(s):  
Perumal Palani ◽  
Tharmalingam Gunasekar ◽  
M. Angayarkanni ◽  
D. Kesavan
Keyword(s):  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Neutral Evolution ◽  
Bounded Linear ◽  
Cosine Families ◽  
Evolution Control ◽  
Evolution Systems

This article, we study sufficient conditions for the controllability of second-order impulsive partial neutral evolution systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
JinRong Wang ◽  
Ahmed G. Ibrahim ◽  
Donal O’Regan ◽  
Adel A. Elmandouh
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Multivalued Function ◽  
Linear Operators ◽  
Solution Set ◽  
Cosine Family ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Noninstantaneous Impulses

AbstractIn this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory.

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