Sufficient conditions for continuous dependence in nonlinear hyperelasticity

1982 ◽  
Vol 12 (2) ◽  
pp. 161-166 ◽  
Author(s):  
Shlomo Breuer ◽  
Marian Aron
Keyword(s):  
Continuous Dependence ◽  
Sufficient Conditions ◽  
Nonlinear Hyperelasticity

scholarly journals Study of the Atangana-Baleanu-Caputo type fractional system with a generalized Mittag-Leffler kernel

2021 ◽  
Vol 7 (2) ◽  
pp. 2001-2018
Author(s):  
Mdi Begum Jeelani ◽  
◽  
Abeer S. Alnahdi ◽  
Mohammed A. Almalahi ◽  
Mohammed S. Abdo ◽  
...  
Keyword(s):  
Fixed Point ◽  
Continuous Dependence ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Fractional Operator ◽  
Stability Of Solutions ◽  
Fractional System ◽  
Mathematical Techniques

<abstract><p>We devote our interest in this work to investigate the sufficient conditions for the existence, uniqueness, and Ulam-Hyers stability of solutions for a new fractional system in the frame of Atangana-Baleanu-Caputo fractional operator with multi-parameters Mittag-Leffler kernels investigated lately by Abdeljawad (Chaos: An Interdisciplinary J. Nonlinear Sci. Vol. 29, no. 2, (2019): 023102). Moreover, the continuous dependence of solution and $ \delta $-approximate solutions are analyzed to such a system. Our approach is based on Banach's and Schaefer's fixed point theorems and some mathematical techniques. In order to illustrate the validity of our results, an example is given.</p></abstract>

scholarly journals The existence and properties of the solution of a class of nonlinear differential equations with switching at variable times

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Huanting Li ◽  
Yunfei Peng ◽  
Kuilin Wu
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Initial State ◽  
Switching Line ◽  
Uniqueness Of The Solution ◽  
The Stability ◽  
Necessary And Sufficient

<p style='text-indent:20px;'>In this paper, we deal with the qualitative theory for a class of nonlinear differential equations with switching at variable times (SSVT), such as the existence and uniqueness of the solution, the continuous dependence and differentiability of the solution with respect to parameters and the stability. Firstly, we obtain the existence and uniqueness of a global solution by defining a reasonable solution (see Definition 2.1). Secondly, the continuous dependence and differentiability of the solution with respect to the initial state and the switching line are investigated. Finally, the global exponential stability of the system is discussed. Moreover, we give the necessary and sufficient conditions of SSVT just switching <inline-formula><tex-math id="M1">\begin{document}$ k\in \mathbb{N} $\end{document}</tex-math></inline-formula> times on bounded time intervals.</p>

scholarly journals A nonstandard Volterra integral equation on time scales

2019 ◽  
Vol 52 (1) ◽  
pp. 503-510 ◽  
Author(s):  
Andrejs Reinfelds ◽  
Shraddha Christian
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Time Scales ◽  
Continuous Dependence ◽  
Sufficient Conditions ◽  
Functional Space ◽  
Volterra Type ◽  
Type Integral ◽  
Banach’S Fixed Point Theorem ◽  
Continuous Dependence Of Solutions

AbstractThis paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.

scholarly journals On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 264
Author(s):  
Mohamed I. Abbas ◽  
Maria Alessandra Ragusa
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Continuous Dependence ◽  
Sufficient Conditions ◽  
New Class ◽  
Hybrid Fixed Point Theorem ◽  
Fractional Differential ◽  
The Given ◽  
Derivatives Of ◽  
Increasing Function

This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function ϑ. By means of a hybrid fixed point theorem for a product of two operators, an existence result is proved. Furthermore, the sufficient conditions of the continuous dependence on the given parameters are investigated. Finally, a simulative example is given to highlight the acquired outcomes.

Positive solutions of nonlinear fourth order iterative differential equations with two-point and integral boundary conditions

2021 ◽  
Vol 8 (1) ◽  
pp. 297-306
Author(s):  
Bouzid Mansouri ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Continuous Dependence ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Iterative Differential Equations

Abstract This paper provides sufficient conditions to guarantee the existence, uniqueness and continuous dependence of positive solutions of a nonlinear fourth order iterative differential equations with two-point and integral boundary conditions. The main arguments are based on the Schauder fixed point theorem to prove the existence of a positive solution. As an application, we given an example to illustrate the obtained results.

scholarly journals On the Weak Solutions of a Delay Composite Functional Integral Equation of Volterra-Stieltjes Type in Reflexive Banach Space

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 245
Author(s):  
Ahmed M. A. El-Sayed ◽  
Yasmin M. Y. Omar
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Continuous Dependence ◽  
Reflexive Banach Space ◽  
Sufficient Conditions ◽  
Functional Integral ◽  
Reflexive Banach Spaces ◽  
Delay Function ◽  
Stieltjes Type ◽  
Differential And Integral Equations

Differential and integral equations in reflexive Banach spaces have gained great attention and hve been investigated in many studies and monographs. Inspired by those, we study the existence of the solution to a delay functional integral equation of Volterra-Stieltjes type and its corresponding delay-functional integro-differential equation in reflexive Banach space E. Sufficient conditions for the uniqueness of the solutions are given. The continuous dependence of the solutions on the delay function, the initial data, and some others parameters are proved.

scholarly journals On a Neutral Itô and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition

2021 ◽  
Vol 5 (4) ◽  
pp. 201
Author(s):  
Ahmed M. A. El-Sayed ◽  
Hoda A. Fouad
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Continuous Dependence ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Condition ◽  
Fractional Orders

In this paper, we are concerned with the combinations of the stochastic Itô-differential and the arbitrary (fractional) orders derivatives in a neutral differential equation with a stochastic, nonlinear, nonlocal integral condition. The existence of solutions will be proved. The sufficient conditions for the uniqueness of the solution will be given. The continuous dependence of the unique solution will be studied.

scholarly journals Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 331 ◽  
Author(s):  
Yu Chen ◽  
JinRong Wang
Keyword(s):  
Fractional Order ◽  
Continuous Dependence ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Impulsive Differential Equations ◽  
Junction Points ◽  
Random Impulse ◽  
Continuous Dependence Results ◽  
Theoretical Results ◽  
Continuous Dependence Of Solutions

This paper gives continuous dependence results for solutions of integer and fractional order, non-instantaneous impulsive differential equations with random impulse and junction points. The notion of the continuous dependence of solutions of these equations on the initial point is introduced. We prove some sufficient conditions that ensure the solutions to perturbed problems have a continuous dependence. Finally, we use numerical examples to demonstrate the obtained theoretical results.

scholarly journals A class of singularly perturbed evolution systems

1994 ◽  
Vol 7 (2) ◽  
pp. 179-190
Author(s):  
N. U. Ahmed
Keyword(s):  
Continuous Dependence ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Singularly Perturbed ◽  
Evolution Operators ◽  
Semilinear Systems ◽  
Existence Of Periodic Solutions ◽  
Semigroup Generators ◽  
Evolution Systems

In this paper we study a class of evolution equations where the semigroup generators are singularly perturbed by a nonnegative real valued function of time. Sufficient conditions for existence of evolution operators and their compactness are given including continuous dependence on the perturbation. Further, for a coupled system of singularly perturbed semilinear systems in two Banach spaces, existence of periodic solutions and their stability are studied.

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