Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space

被引：5

作者：

Chang, Yong-Kui ^{[1
]}

Zhao, Zhi-Han ^{[1
]}

N'Guerekata, Gaston Mandata ^{[2
]}

机构：

[1] Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

[2] Morgan State Univ, Dept Math, Baltimore, MD 21251 USA

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2011年

关键词：

Stochastic differential equations; Square-mean almost automorphic processes; Mild solutions; ALMOST-PERIODIC SOLUTIONS; EXISTENCE;

D O I：

10.1186/1687-1847-2011-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article deals primarily with the existence and uniqueness of square-mean almost automorphic mild solutions for a class of stochastic differential equations in a real separable Hilbert space. We study also some properties of square-mean almost automorphic functions including a compostion theorem. To establish our main results, we use the Banach contraction mapping principle and the techniques of fractional powers of an operator.

引用

页数：12

共 50 条

[31] Square-mean inertial manifolds for stochastic differential equations
Thi Oanh Le
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2022, 30 (02) : 149 - 159
[32] SQUARE-MEAN ALMOST AUTOMORPHIC SOLUTION OF A STOCHASTIC CELLULAR NEURAL NETWORK ON TIME SCALES
Dhama, Soniya
Abbas, Syed
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2020, 32 (02) : 151 - 170
[33] Existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations
Sakthivel, R.
Revathi, P.
Anthoni, S. Marshal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (07) : 3339 - 3347
[34] Mean-Square Asymptotically Almost Automorphic Solutions to Fractional Stochastic Relaxation Equations
Wu, Qiong
INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 2015
[35] EXISTENCE OF STEPANOV-LIKE SQUARE-MEAN PSEUDO ALMOST PERIODIC SOLUTIONS TO PARTIAL STOCHASTIC NEUTRAL DIFFERENTIAL EQUATIONS
Yan, Zuomao
Zhang, Hongwu
ANNALS OF FUNCTIONAL ANALYSIS, 2015, 6 (01): : 116 - 138
[36] ALMOST AUTOMORPHIC SOLUTIONS OF NONAUTONOMOUS STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS IN HILBERT SPACES
Xia, Zhinan
Wen, Ching-Feng
Wang, Dingjiang
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2016, 17 (04) : 841 - 851
[37] Almost automorphic mild solutions to fractional differential equations
Araya, Daniela
Lizama, Carlos
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (11) : 3692 - 3705
[38] Square-mean asymptotically almost periodic solutions of second order nonautonomous stochastic evolution equations
Liu, Jinghuai
Zhang, Litao
AIMS MATHEMATICS, 2021, 6 (05): : 5040 - 5052
[39] Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to semi-linear differential equations in Hilbert spaces
Yong-Kui Chang
Zhi-Han Zhao
Juan J. Nieto
Revista Matemática Complutense, 2011, 24 : 421 - 438
[40] ALMOST AUTOMORPHIC SOLUTIONS OF SEMILINEAR STOCHASTIC HYPERBOLIC DIFFERENTIAL EQUATIONS IN INTERMEDIATE SPACE
Xia, Zhinan
KODAI MATHEMATICAL JOURNAL, 2017, 40 (03) : 492 - 517

← 1 2 3 4 5 →