scholarly journals Nonlinear Impulsive Differential Equations with Weighted Exponential or Ordinary Dichotomous Linear Part in a Banach Space

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Hristo Kiskinov ◽  
Andrey Zahariev
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Bounded Solutions ◽  
Fixed Point Principle

We consider nonlinear impulsive differential equations withψ-exponential andψ-ordinary dichotomous linear part in a Banach space. By the help of Banach’s fixed-point principle sufficient conditions are found for the existence ofψ-bounded solutions of these equations onRandR+.

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals Bifurcation of Bounded Solutions of Impulsive Differential Equations

2016 ◽  
Vol 26 (14) ◽  
pp. 1650242 ◽  
Author(s):  
Kevin E. M. Church ◽  
Xinzhi Liu
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Necessary Condition ◽  
Bounded Solutions ◽  
Pitchfork Bifurcations ◽  
Nonlinear Integral Operator

In this article, we examine nonautonomous bifurcation patterns in nonlinear systems of impulsive differential equations. The approach is based on Lyapunov–Schmidt reduction applied to the linearization of a particular nonlinear integral operator whose zeroes coincide with bounded solutions of the impulsive differential equation in question. This leads to sufficient conditions for the presence of fold, transcritical and pitchfork bifurcations. Additionally, we provide a computable necessary condition for bifurcation in nonlinear scalar impulsive differential equations. Several examples are provided illustrating the results.

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

scholarly journals Lp-equivalence of a linear and a nonlinear impulsive differential equation in a Banach space

1993 ◽  
Vol 36 (1) ◽  
pp. 17-33 ◽  
Author(s):  
D. D. Bainov ◽  
S. I. Kostadinov ◽  
P. P. Zabreiko
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations

In the present paper by means of the Schauder-Tychonoff principle sufficient conditions are obtained for Lp-equivalence of a linear and a nonlinear impulsive differential equations.

scholarly journals EXISTENCE OF NONOSCILLATORY RELATIVELY BOUNDED SOLUTIONS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS

2019 ◽  
Vol 11 (2) ◽  
pp. 63-71
Author(s):  
Bashar Ahmed Jawad Sharba ◽  
Hussain Ali Mohamad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Convergence Theorem ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Differential Equations ◽  
Existence Of Positive Solutions ◽  
Dominated Convergence

In this paper some sufficient conditions are obtained to insure the existence of positive solutions which is relatively bounded from one side for nonlinear neutral differential equations of second order.Weused the Krasnoselskii’s fixed point theorem and Lebesgue’s dominated convergence theorem to obtain new sufficient conditions for the existence of a Nonoscillatoryone side relatively boundedsolutions.These conditions are more applicable than some known results in the references. Three examples included to illustrate the results obtained.

scholarly journals An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Asma Bouzaroura ◽  
Saïd Mazouzi
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Nonlocal Condition ◽  
Impulsive Differential Equations ◽  
Fractional Equations ◽  
Contraction Theorem ◽  
Fractional Orders ◽  
Stability Of The Solution

This paper is concerned with the existence, uniqueness, and stability of the solution of some impulsive fractional problem in a Banach space subjected to a nonlocal condition. Meanwhile, we give a new concept of a solution to impulsive fractional equations of multiorders. The derived results are based on Banach's contraction theorem as well as Schaefer's fixed point theorem.

scholarly journals On Nonlinear Forced Impulsive Differential Equations under Canonical and Non-Canonical Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2066
Author(s):  
Shyam Sundar Santra ◽  
Hammad Alotaibi ◽  
Samad Noeiaghdam ◽  
Denis Sidorov
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Impulsive System ◽  
Bounded Solutions ◽  
Oscillatory Behaviour ◽  
Impulsive Systems ◽  
Forcing Term

This study is connected with the nonoscillatory and oscillatory behaviour to the solutions of nonlinear neutral impulsive systems with forcing term which is studied for various ranges of of the neutral coefficient. Furthermore, sufficient conditions are obtained for the existence of positive bounded solutions of the impulsive system. The mentioned example shows the feasibility and efficiency of the main results.

scholarly journals Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xingru Chen ◽  
Haibo Gu ◽  
Yu Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Optimal Controls ◽  
Minimizing Sequences ◽  
Fractional Differential

In this paper, we investigate a class of impulsive Katugampola fractional differential equations with nonlocal conditions in a Banach space. First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. Secondly, we derive the sufficient conditions for optimal controls by building approximating minimizing sequences of functions twice.

Sign in / Sign up

Export Citation Format

Share Document