scholarly journals Controllability of Nonlinear Neutral Stochastic Differential Inclusions with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yong Li ◽  
Qiang Zou
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Stochastic Differential Inclusions ◽  
Condensing Maps

The paper is concerned with the controllability of nonlinear neutral stochastic differential inclusions with infinite delay in a Hilbert space. Sufficient conditions for the controllability are obtained by using a fixed-point theorem for condensing maps due to O'Regan.

ALMOST PERIODICITY IN AN IMPULSIVE LOGISTIC EQUATION WITH INFINITE DELAY

2008 ◽  
Vol 01 (03) ◽  
pp. 355-360 ◽  
Author(s):  
CHUNHUA FENG ◽  
ZHENKUN HUANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Logistic Equation ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic

By employing a fixed point theorem in cones, this paper investigates the existence of almost periodic solutions for an impulsive logistic equation with infinite delay. A set of sufficient conditions on the existence of almost periodic solutions of the equation is obtained.

scholarly journals Null controllability of neutral evolution integrodifferential systems with infinite delay

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
K. Balachandran ◽  
A. Leelamani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Null Controllability ◽  
Neutral Evolution ◽  
Sadovskii Fixed Point Theorem

We establish a set of sufficient conditions for the controllability of nonlinear neutral evolution integrodifferential systems with infinite delay in Banach spaces. The results are established by using the Sadovskiĭ fixed point theorem and generalize the previous results.

scholarly journals On a nonlocal Cauchy problem for differential inclusions

2004 ◽  
Vol 2004 (5) ◽  
pp. 425-434 ◽  
Author(s):  
E. Gatsori ◽  
S. K. Ntouyas ◽  
Y. G. Sficas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Lower Semicontinuous ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Multivalued Operators ◽  
Nonlocal Cauchy Problem

We establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values.

Controllability of Sobolev Type Semilinear Functional Differential and Integrodifferential Inclusions with an Unbounded Delay

2006 ◽  
Vol 13 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Yong-Kui Chang ◽  
Wan-Tong Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Unbounded Delay ◽  
Functional Differential ◽  
The Fixed Point Theorem ◽  
Condensing Maps

Abstract In this paper, sufficient conditions are established for the controllability of Sobolev type semilinear functional differential and integrodifferential inclusions with an unbounded delay in Banach spaces. The main results are obtained by using the fixed point theorem for condensing maps due to Martelli.

scholarly journals A method of upper and lower solutions for functional differential inclusions

2002 ◽  
Vol 15 (3) ◽  
pp. 269-276
Author(s):  
Mouffak Benchohra ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Upper And Lower Solutions ◽  
First Order ◽  
Functional Differential ◽  
Functional Differential Inclusions ◽  
Condensing Maps

In this paper, a fixed point theorem for condensing maps combined with upper and lower solutions are used to investigate the existence of solutions for first order functional differential inclusions.

EXISTENCE AND CONTROLLABILITY RESULTS FOR INFINITE DELAY PARTIAL FUNCTIONAL DIFFERENTIAL SYSTEMS WITH MULTI-VALUED IMPULSES IN BANACH SPACES

2010 ◽  
Vol 03 (04) ◽  
pp. 631-646 ◽  
Author(s):  
Hanwen Ning ◽  
Bing Liu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential

This paper is concerned with the existence and controllability of solutions for infinite delay functional differential systems with multi-valued impulses in Banach space. Sufficient conditions for the existence are obtained by using a fixed point theorem for multi-valued maps due to Dhage. An example is also given to illustrate our results.

scholarly journals Existence and Controllability Results for Mixed Functional Integrodifferential Equations with Infinite Delay

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Kishor D. Kucche
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Integrodifferential Equations ◽  
Fractional Powers ◽  
Fractional Powers Of Operators ◽  
Controllability Result

AbstractSufficient conditions are established for the existence of solution for mixed neutral functional integrodifferential equations with infinite delay. The results are obtained using the theory of fractional powers of operators and the Sadovskii’s fixed point theorem. As an application we prove a controllability result for the system.

scholarly journals Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
X. J. Wan ◽  
Y. P. Zhang ◽  
J. T. Sun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Controllability Problem ◽  
Special Cases ◽  
Functional Differential ◽  
Functional Differential Inclusions

We investigate the controllability of impulsive neutral functional differential inclusions in Banach spaces. Our main aim is to find an effective method to solve the controllability problem of impulsive neutral functional differential inclusions with multivalued jump sizes in Banach spaces. Based on a fixed point theorem with regard to condensing map, sufficient conditions for the controllability of the impulsive neutral functional differential inclusions in Banach spaces are derived. Moreover, a remark is given to explain less conservative criteria for special cases, and work is improved in the previous literature.

scholarly journals Approximate controllability of neutral delay integro-differential inclusion of order $ \alpha\in (1, 2) $ with non-instantaneous impulses

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Avadhesh Kumar ◽  
Ankit Kumar ◽  
Ramesh Kumar Vats ◽  
Parveen Kumar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Control Problem ◽  
Resolvent Operator ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
The Fixed Point Theorem

<p style='text-indent:20px;'>This paper aims to establish the approximate controllability results for fractional neutral integro-differential inclusions with non-instantaneous impulse and infinite delay. Sufficient conditions for approximate controllability have been established for the proposed control problem. The tools for study include the fixed point theorem for discontinuous multi-valued operators with the <inline-formula><tex-math id="M3">\begin{document}$ \alpha- $\end{document}</tex-math></inline-formula>resolvent operator. Finally, the proposed results are illustrated with the help of an example.</p>

scholarly journals Controllability for neutral stochastic functional integrodifferential equations with infinite delay

2016 ◽  
Vol 1 (2) ◽  
pp. 493-506 ◽  
Author(s):  
Tomás Caraballo ◽  
Mamadou Abdoul Diop ◽  
Aziz Mane
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Separable Hilbert Space ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Resolvent Operators ◽  
Real Separable Hilbert Space ◽  
Stochastic Functional

AbstractIn this work, we study the controllability for a class of nonlinear neutral stochastic functional integrodifferential equations with infinite delay in a real separable Hilbert space. Sufficient conditions for the controllability are established by using Nussbaum fixed point theorem combined with theories of resolvent operators. As an application, an example is provided to illustrate the obtained result.

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