scholarly journals EXISTENCE AND STABILITY OF ALMOST PERIODIC SOLUTIONS TO IMPULSIVE STOCHASTIC DIFFERENTIAL EQUATIONS

Cubo (Temuco) ◽  
2013 ◽  
Vol 15 (1) ◽  
pp. 77-96 ◽  
Author(s):  
Junwei Liu ◽  
Chuanyi Zhang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Existence And Stability

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 Almost Periodic Solutions of First-Order Ordinary Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 171 ◽  
Author(s):  
Seifedine Kadry ◽  
Gennady Alferov ◽  
Gennady Ivanov ◽  
Artem Sharlay
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Upper And Lower Bounds ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
First Order ◽  
Existence And Stability ◽  
Solutions Of Equations ◽  
The Right

Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are studied. The novelty of this paper lies in the fact that the use of apparatus derivatives allows for the reduction of restrictions on the degree of smoothness of the right parts. In the works of Lebedeva [1], regarding the number of periodic solutions of equations first order, they required a high degree of smoothness. Franco et al. required the smoothness of the second derivative of the Schwartz equation [2]. We have all of these restrictions lifted. Our new form presented also emphasizes this novelty.

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.

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