scholarly journals Existence and stability of solutions of $ \psi $-Hilfer fractional functional differential inclusions with non-instantaneous impulses

2021 ◽  
Vol 6 (10) ◽  
pp. 10802-10832
Author(s):  
A.G. Ibrahim ◽  
◽  
A.A. Elmandouh ◽  
Keyword(s):  
Stability Of Solutions ◽  
Picard Operator ◽  
Infinite Dimensional ◽  
Existence And Stability ◽  
Fractional Integral Equation ◽  
Functional Differential ◽  
The Stability ◽  
Weakly Picard Operator ◽  
The Given ◽  
Functional Differential Inclusions

<abstract><p>In this paper, we prove two existence results of solutions for an $ \psi $-Hilfer fractional non-instantaneous impulsive differential inclusion in the presence of delay in an infinite dimensional Banah spaces. Then, by using the multivalued weakly Picard operator theory, we study the stability of solutions for the considered problem in the sense of $ \psi $-generalized Ulam-Hyers. To achieve our aim, we present a relation between any solution of the considered problem and the corresponding fractional integral equation. The given problem here is new because it contains a delay and non-instantaneous impulses effect. Examples are given to clarify the possibility of applicability our assumptions.</p></abstract>

scholarly journals Existence and Stability of Solutions of General Semilinear Elliptic Equations with Measure Data

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Laurent Véron
Keyword(s):  
Elliptic Equations ◽  
Measure Data ◽  
Unified Theory ◽  
Stability Of Solutions ◽  
Semilinear Elliptic ◽  
The Poisson Equation ◽  
Order Elliptic Operator ◽  
Carathéodory Function ◽  
Existence And Stability ◽  
The Stability

AbstractWe study existence and stability for solutions of −Lu + g(x, u) = ω where L is a second order elliptic operator, g a Caratheodory function and ω a measure in Ω. We present a unified theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.

scholarly journals A study of a system of operator inclusions via a fixed point approach and applications to functional-differential inclusions

2016 ◽  
Vol 32 (3) ◽  
pp. 349-361 ◽  
Author(s):  
ADRIAN PETRUSEL ◽  
◽  
GABRIELA PETRUSEL ◽  
JEN-CHIH YAO ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Metric Spaces ◽  
Mixed Boundary ◽  
Cartesian Product ◽  
Qualitative Properties ◽  
Initial Value ◽  
Functional Differential ◽  
The Given ◽  
Functional Differential Inclusions

In this paper, some existence results for a system of operator inclusions are presented. Qualitative properties of the solution set are also discussed. The method is based on the application of a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces. The approach is new even for the case of the metric spaces. As an application, an existence result for a mixed boundary and initial value problem for a system of second order differential inclusions is given.

scholarly journals Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations

1996 ◽  
Vol 1 (4) ◽  
pp. 351-380 ◽  
Author(s):  
Bernd Aulbach ◽  
Nguyen Van Minh
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Stability Of Solutions ◽  
Nonlinear Operators ◽  
Nonlinear Semigroups ◽  
Evolution Semigroup ◽  
Existence And Stability ◽  
Functional Differential

This paper is concerned with the existence and stability of solutions of a class of semilinear nonautonomous evolution equations. A procedure is discussed which associates to each nonautonomous equation the so-called evolution semigroup of (possibly nonlinear) operators. Sufficient conditions for the existence and stability of solutions and the existence of periodic oscillations are given in terms of the accretiveness of the corresponding infinitesimal generator. Furthermore, through the existence of integral manifolds for abstract evolutionary processes we obtain a reduction principle for stability questions of mild solutions. The results are applied to a class of partial functional differential equations.

scholarly journals Existence and Exponential Stability of Solutions to Stochastic Neutral Functional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Ling Hu ◽  
Zheng Wu ◽  
Zhangzhi Wei ◽  
Lianglong Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Banach Fixed Point Theorem ◽  
Stability Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Semigroup Approach ◽  
Existence And Stability ◽  
Functional Differential

In this paper we consider the existence and stability of solutions to stochastic neutral functional differential equations with finite delays. Under suitable conditions, the existence and exponential stability of solutions were obtained by using the semigroup approach and Banach fixed point theorem.

scholarly journals Stability to a Kind of Functional Differential Equations of Second Order with Multiple Delays by Fixed Points

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Cemil Tunç ◽  
Emel Biçer
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Differential Equations ◽  
Multiple Delays ◽  
Stability Of Solutions ◽  
Variable Delays ◽  
Multiple Variable ◽  
Fixed Point Technique ◽  
Functional Differential ◽  
The Stability

We discuss the stability of solutions to a kind of scalar Liénard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays.

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