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.

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.

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.

Periodic Solutions of Second Order Degenerate Differential Equations with Delay in Banach Spaces

2018 ◽  
Vol 61 (4) ◽  
pp. 717-737 ◽  
Author(s):  
Shangquan Bu ◽  
Gang Cai
Keyword(s):  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Order Degenerate ◽  
Degenerate Differential Equations ◽  
Necessary And Sufficient ◽  
Equations With Delay ◽  
Closed Linear Operators

AbstractWe give necessary and sufficient conditions of the Lp-well-posedness (resp. -wellposedness) for the second order degenerate differential equation with finite delayswith periodic boundary conditions (Mu)(0) = (Mu)(2π), (Mu)′ (0) = (Mu)′ (2π), where A, B, and M are closed linear operators on a complex Banach space X satisfying D(A) ∩ D(B) ⊂ D(M), F and G are bounded linear operators from into X.

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 Holder's Inequality ρ–Mean Continuity for Existence and Uniqueness Solution of Fractional Multi-Integrodifferential Delay System

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Sameer Qasim Hasan
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Infinite Delay ◽  
Hölder’S Inequality ◽  
Sufficient Conditions ◽  
Delay System ◽  
Linear Operators ◽  
Bounded Linear ◽  
Hölder's Inequality

We herein present the detailed results for the existence and uniqueness of mild solution for multifractional order impulsive integrodifferential control equations with a nonlocal condition involving several types of semigroups of bounded linear operators, which were established on probability density functions related with the fractional differential equation. Additionally, we present the necessary and sufficient conditions to investigate Schauder’s fixed point theorem with Holder’s inequality ρ–mean continuity and infinite delay parameter to guarantee the uniqueness of a fixed point.

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.

Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution

2020 ◽  
Author(s):  
Surendra Kumar ◽  
Syed Mohammad Abdal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Existence Of A Solution ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class

Abstract This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

scholarly journals Positive functionals and oscillation criteria for second order differential systems

1979 ◽  
Vol 22 (3) ◽  
pp. 277-290 ◽  
Author(s):  
Garret J. Etgen ◽  
Roger T. Lewis
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Second Order ◽  
Linear Operators ◽  
The Self ◽  
Differential Systems ◽  
Bounded Linear ◽  
Positive Functionals ◽  
Image Position ◽  
Adjoint Operators

Let ℋ be a Hilbert space, let ℬ = (ℋ, ℋ) be the B*-algebra of bounded linear operators from ℋ to ℋ with the uniform operator topology, and let ℒ be the subset of ℬ consisting of the self-adjoint operators. This article is concerned with the second order self-adjoint differential equation

Sign in / Sign up

Export Citation Format

Share Document