scholarly journals Asymptotically almost automorphic solutions of differential equations with piecewise constant argument

2017 ◽  
Vol 15 (1) ◽  
pp. 595-610
Author(s):  
Hui-Sheng Ding ◽  
Shun-Mei Wan
Keyword(s):  
Differential Equations ◽  
Uniqueness Theorem ◽  
Systematic Study ◽  
Existence And Uniqueness ◽  
Difference System ◽  
Existence And Uniqueness Theorem ◽  
Piecewise Constant ◽  
Almost Automorphic ◽  
Piecewise Constant Argument ◽  
Constant Argument

Abstract This paper is concerned with the existence and uniqueness of asymptotically almost automorphic solutions to differential equations with piecewise constant argument. To study that, we first introduce several notions about asymptotically almost automorphic type functions and obtain some properties of such functions. Then, on the basis of a systematic study on the associated difference system, the existence and uniqueness theorem is established. Compared with some earlier results, we do not assume directly that the Green’s function is a Bi-almost automorphic type function.

scholarly journals ALMOST AUTOMORPHIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

2013 ◽  
Vol 90 (1) ◽  
pp. 99-112 ◽  
Author(s):  
LI-LI ZHANG ◽  
HONG-XU LI
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Piecewise Constant ◽  
Exponential Dichotomies ◽  
Almost Automorphic ◽  
Piecewise Constant Argument ◽  
Greatest Integer Function ◽  
Image Position ◽  
Constant Argument

AbstractUsing the method of exponential dichotomies, we establish a new existence and uniqueness theorem for almost automorphic solutions of differential equations with piecewise constant argument of the form $$\begin{eqnarray*}{x}^{\prime } (t)= A(t)x(t)+ B(t)x(\lfloor t\rfloor )+ f(t), \quad t\in \mathbb{R} ,\end{eqnarray*}$$ where $\lfloor \cdot \rfloor $ denotes the greatest integer function, and $A(t), B(t): \mathbb{R} \rightarrow { \mathbb{R} }^{q\times q} $, $f(t): \mathbb{R} \rightarrow { \mathbb{R} }^{q} $ are all almost automorphic.

scholarly journals Fuzzy Conformable Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Fractional Differential ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

scholarly journals A Picard Theorem for iterative differential equations

2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Wen-rong Li ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Picard Theorem ◽  
Iterative Differential Equations

AbstractA Picard type existence and uniqueness theorem is established for iterative differential equations of the form

scholarly journals Existence and uniqueness theorem for a solution of fuzzy differential equations

1999 ◽  
Vol 22 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Jong Yeoul Park ◽  
Hyo Keun Han
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of A Solution

By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equationx′(t)=f(t,x(t)),x(t0)=x0. We also consider anϵ-approximate solution of the above fuzzy differential equation.

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