scholarly journals Existence Results for Semilinear Functional Differential System with Nonlocal Conditions

2018 ◽  
Vol 8 (10S) ◽  
pp. 237-241
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Abstract Space ◽  
Functional Differential ◽  
Functional Differential System

In this paper, sufficient conditions are given for the existence of partial functional differential equations with nonlocal conditions in an abstract space with the help of the fixed point theorems.

EXISTENCE RESULTS FOR NONDENSELY DEFINED IMPULSIVE SEMILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2008 ◽  
Vol 01 (04) ◽  
pp. 449-468 ◽  
Author(s):  
Nadjet Abada ◽  
Ravi P. Agarwal ◽  
Mouffak Benchohra ◽  
Hadda Hammouche
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Completely Continuous ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Integral Solutions

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined impulsive semilinear functional differential equations with state-dependent delay in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators.

The Existence of Solutions for Fractional Functional Differential Equations With Boundary Value Conditions

2011 ◽  
Author(s):  
Chunhai Kou ◽  
Huacheng Zhou ◽  
Sijia Wu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

In this paper, we are concerned with the existence of solutions for a class of nonlinear fractional functional differential equations with boundary value conditions. Some existence results of solutions are obtained. Our analysis relies on some fixed point theorems. Finally, some examples are presented to illustrate the main results.

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.

scholarly journals Some Existence Results for Systems of Impulsive Stochastic Differential Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sliman Mekki ◽  
Tayeb Blouhi ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Impulsive Systems ◽  
Uniqueness Of Solutions

Abstract In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.

scholarly journals J-nonexpansive mappings in uniform spaces and applications

1991 ◽  
Vol 43 (2) ◽  
pp. 331-339 ◽  
Author(s):  
Vasil G. Angelov
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Functional Differential Equations ◽  
Uniform Convexity ◽  
Existence Theory ◽  
Uniform Spaces ◽  
Geometric Properties ◽  
Functional Differential

The purpose of the paper is to introduce a class of “j-nonexpansive” mappings and to prove fixed point theorems for such mappings. They naturally arise in the existence theory of functional differential equations. These mappings act in spaces without specific geometric properties as, for instance, uniform convexity. Critical examples are given.

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.

scholarly journals Smooth Solutions of a Class of Iterative Functional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Houyu Zhao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Smooth Solutions ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

By Faà di Bruno’s formula, using the fixed-point theorems of Schauder and Banach, we study the existence and uniqueness of smooth solutions of an iterative functional differential equationx′(t)=1/(c0x[0](t)+c1x[1](t)+⋯+cmx[m](t)).

Anti-periodic solutions of nonlinear first order impulsive functional differential equations

2012 ◽  
Vol 62 (4) ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Existence Results ◽  
First Order ◽  
Functional Differential

AbstractThe existence of anti-periodic solutions of the following nonlinear impulsive functional differential equations $$ x'(t) + a(t)x(t) = f(t,x(t),x(\alpha _1 (t)), \ldots ,x(\alpha _n (t))),t \in \mathbb{R},\Delta x(t_k ) = I_k (x(t_k )),k \in \mathbb{Z} $$ is studied. Sufficient conditions for the existence of at least one anti-periodic solution of the mentioned equation are established. Several new existence results are obtained.

Fuzzy Solutions for Neutral Functional Differential Equations with Nonlocal Conditions

2004 ◽  
Vol 11 (1) ◽  
pp. 35-42
Author(s):  
Amaria Arara ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Banach Fixed Point Theorem ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fuzzy Solutions

Abstract The Banach fixed point theorem is used to investigate the existence of fuzzy solutions for first and second order neutral functional differential equations with nonlocal conditions.

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

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