scholarly journals First-order impulsive differential systems: sufficient and necessary conditions for oscillatory or asymptotic behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Dumitru Baleanu ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
First Order ◽  
Impulsive Differential Systems ◽  
Sufficient And Necessary Conditions

AbstractIn this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results.

scholarly journals Controllability of nonlocal non-autonomous neutral differential systems including non-instantaneous impulsive effects in 𝕉n

2020 ◽  
Vol 28 (3) ◽  
pp. 103-121
Author(s):  
Velusamy Kavitha ◽  
Mani Mallika Arjunan ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Evolution Family ◽  
Impulsive Effects ◽  
Differential Systems ◽  
First Order ◽  
Set Up

AbstractThis manuscript involves a class of first-order controllability results for nonlocal non-autonomous neutral differential systems with non-instantaneous impulses in the space 𝕉n. Sufficient conditions guaranteeing the controllability of mild solutions are set up. Concept of evolution family and Rothe’s fixed point theorem are employed to achieve the required results. A model is investigated to delineate the adequacy of the results.

scholarly journals Second-Order Impulsive Delay Differential Systems: Necessary and Sufficient Conditions for Oscillatory or Asymptotic Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 722
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz ◽  
Ali Muhib ◽  
Shao-Wen Yao
Keyword(s):  
Asymptotic Behavior ◽  
Differential System ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Impulsive Delay ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient

In this work, we aimed to obtain sufficient and necessary conditions for the oscillatory or asymptotic behavior of an impulsive differential system. It is easy to notice that most works that study the oscillation are concerned only with sufficient conditions and without impulses, so our results extend and complement previous results in the literature. Further, we provide two examples to illustrate the main results.

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 Approximate Controllability of Fractional Nonlinear Hybrid Differential Systems via Resolvent Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Mohammed M. Matar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential System ◽  
Point Theorem ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Resolvent Operators ◽  
Differential Systems ◽  
Sectorial Operators ◽  
Nonlinear Hybrid

We obtain sufficient conditions for the approximate controllability of a fractional nonlinear hybrid differential system. The results are obtained by using resolvent and sectorial operators technique via Dhage fixed point theorem.

scholarly journals Controllability of Differential Systems with the General Conformable Derivative

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ferrag Azouz ◽  
Djalal Boucenna ◽  
Abdellatif Ben Makhlouf ◽  
Lassaad Mchiri ◽  
Abbes Benchaabane
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Necessary Conditions ◽  
Order System ◽  
Complete Controllability ◽  
Conformable Derivative ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Controllability Result

In this paper, the controllability of differential systems with the general conformable derivative is studied. By elaborating the rank criterion and the conformable Gram criterion, sufficient and necessary conditions to investigate that a linear general conformable system is null completely controllable are given. We obtain a full generalization to the general conformable fractional-order system case. In addition, Krasnoselskii’s fixed point theorem to obtain a complete controllability result for a semilinear general conformable system is applied.

scholarly journals Schauder’s fixed-point theorem in approximate controllability problems

2016 ◽  
Vol 26 (2) ◽  
pp. 263-275 ◽  
Author(s):  
Artur Babiarz ◽  
Jerzy Klamka ◽  
Michał Niezabitowski
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Differential Systems ◽  
Schauder's Fixed Point Theorem

AbstractThe main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.

scholarly journals New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 934
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Kamsing Nonlaopon ◽  
Hijaz Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Discrete Equation ◽  
Qualitative Behavior ◽  
Differential Systems ◽  
Impulsive Differential Systems

The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included.

scholarly journals Existence of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

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