scholarly journals Mean Square Almost Periodic Solutions for Impulsive Stochastic Differential Equations with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ruojun Zhang ◽  
Nan Ding ◽  
Linshan Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Mean Square ◽  
Almost Periodic Solutions ◽  
Almost Periodic

We establish a result on existence and uniqueness on mean square almost periodic solutions for a class of impulsive stochastic differential equations with delays, which extends some earlier works reported in the literature.

Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay

2019 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
Xiao Ma ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Infinite Delay ◽  
Almost Periodic Solutions ◽  
Almost Periodic

In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results.

scholarly journals Eberlein weak almost periodic solutions for a class of integro-differential equations with infinite delay

2018 ◽  
Vol 5 (1) ◽  
pp. 127-137
Author(s):  
Khalil Ezzinbi ◽  
Samir Fatajou ◽  
Fatima Zohra Elamrani
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Weakly Almost Periodic

AbstractIn thiswork,we provide sufficient conditions ensuring the existence and uniqueness of an Eberlein weakly almost periodic solutions for some semilinear integro-differential equations with infinite delay in Banach spaces. For illustration, we provide an example arising in viscoelasticity theory.

scholarly journals Ergodicity and asymptotically almost periodic solutions of some differential equations

2001 ◽  
Vol 25 (12) ◽  
pp. 787-801 ◽  
Author(s):  
Chuanyi Zhang
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Ergodic Condition ◽  
Asymptotically Almost Periodic

Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped.

scholarly journals Remotely Almost Periodic Solutions of Ordinary Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
C. Maulén ◽  
S. Castillo ◽  
M. Kostić ◽  
M. Pinto
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Exponential Dichotomy ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Homogeneous Part

In this paper, we analyze the existence and uniqueness of remotely almost periodic solutions for systems of ordinary differential equations. The existence and uniqueness of remotely almost periodic solutions are achieved by using the results about the exponential dichotomy and the Bi-almost remotely almost periodicity of the homogeneous part of the corresponding systems of ordinary differential equations under our consideration.

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