Anti-periodic mild solutions for some functional integro-differential equations with infinite delay

2018 ◽  
Vol 12 (21) ◽  
pp. 1021-1033
Author(s):  
Cheng Huang ◽  
Weibin Liu
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

scholarly journals The Kneser property for abstract retarded functional differential equations with infinite delay

2003 ◽  
Vol 2003 (26) ◽  
pp. 1645-1661 ◽  
Author(s):  
Hernán R. Henríquez
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
First Order ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

We establish existence of mild solutions for a class of semilinear first-order abstract retarded functional differential equations (ARFDEs) with infinite delay and we prove that the set consisting of mild solutions for this problem is connected in the space of continuous functions.

scholarly journals Well posedness results for higher-order neutral stochastic differential equations driven by Poisson jumps and Rosenblatt process

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 353-365
Author(s):  
K. Ramkumar ◽  
K. Ravikumar ◽  
A. Anguraj ◽  
Hamdy Ahmed
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Successive Approximation Method ◽  
Poisson Jumps ◽  
Rosenblatt Process

In this article, we investigate the existence, uniqueness and stability of mild solutions for a class of higher-order nonautonomous neutral stochastic differential equations (NSDEs) with infinite delay driven by Poisson jumps and Rosenblatt process in Hilbert space. More precisely, using semigroup theory and successive approximation method, we establish a set of sufficient conditions for obtained the required result. Further, the result is deduced to study the higher-order autonomous system. Finally, examples are provided to demonstrate the obtain results.

scholarly journals Existence and Stability for Stochastic Partial Differential Equations with Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan ◽  
Xichao Sun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Partial Differential ◽  
Sample Paths ◽  
Existence And Stability ◽  
Stability In Mean Square

We consider a class of neutral stochastic partial differential equations with infinite delay in real separable Hilbert spaces. We derive the existence and uniqueness of mild solutions under some local Carathéodory-type conditions and also exponential stability in mean square of mild solutions as well as its sample paths. Some known results are generalized and improved.

scholarly journals EXISTENCE OF S-ASYMPTOTICALLY ω-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS

2008 ◽  
Vol 78 (3) ◽  
pp. 365-382 ◽  
Author(s):  
HERNÁN R. HENRÍQUEZ ◽  
MICHELLE PIERRI ◽  
PLÁCIDO TÁBOAS
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Qualitative Properties ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Bounded Continuous Function ◽  
Functional Differential

AbstractA bounded continuous function $u:[0,\infty )\to X$ is said to be S-asymptotically ω-periodic if $ \lim _{t\to \infty }[ u(t+\omega ) -u(t)]=0$. This paper is devoted to study the existence and qualitative properties of S-asymptotically ω-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given.

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