Square-mean piecewise almost automorphic mild solutions to a class of impulsive stochastic evolution equations

被引：1

作者：

Liu, Junwei ^{[1
]}

Ren, Ruihong ^{[1
]}

Xie, Rui ^{[2
]}

机构：

[1] Yanshan Univ, Coll Sci, Qinhuangdao, Hebei, Peoples R China

[2] Tianjin Univ Commerce, Dept Math, Tianjin, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Square-mean piecewise almost automorphic function; Theory of semigroups of operators; Contraction mapping principle; Impulsive stochastic evolution equations; Generalized Gronwall-Bellman inequality; NICHOLSONS BLOWFLIES MODEL; ALMOST-PERIODIC SOLUTIONS;

D O I：

10.1186/s13662-020-02574-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the concept of square-mean piecewise almost automorphic function. By using the theory of semigroups of operators and the contraction mapping principle, the existence of square-mean piecewise almost automorphic mild solutions for linear and nonlinear impulsive stochastic evolution equations is investigated. In addition, the exponential stability of square-mean piecewise almost automorphic mild solutions for nonlinear impulsive stochastic evolution equations is obtained by the generalized Gronwall-Bellman inequality. Finally, we provide an illustrative example to justify the results.

引用

页数：19

共 47 条

[21] Almost Automorphic Solutions to Nonautonomous Stochastic Functional Integrodifferential Equations [J].

Li Xi-liang ;

Han Yu-liang .

ABSTRACT AND APPLIED ANALYSIS, 2013,

[22] Existence and exponential stability of piecewise mean-square almost periodic solutions for impulsive stochastic Nicholson's blowflies model on time scales [J].

Wang, Chao .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 248 :101-112

[23] Almost automorphic solutions for mean-field stochastic differential equations driven by fractional Brownian motion [J].

Chen, Feng ;

Zhang, Xiaoying .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2019, 37 (01) :1-18

[24] Almost automorphic solutions for stochastic differential equations driven by Levy noise [J].

Liu, Zhenxin ;

Sun, Kai .

JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (03) :1115-1149

[25] Mean-Square Almost Periodic Solutions for Impulsive Stochastic Host-Macroparasite Equation on Time Scales [J].

Wang, Pan ;

Lin, Qingmei ;

Li, Yongkun .

DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2015, 2015

[26] Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to semi-linear differential equations in Hilbert spaces [J].

Chang, Yong-Kui ;

Zhao, Zhi-Han ;

Nieto, Juan J. .

REVISTA MATEMATICA COMPLUTENSE, 2011, 24 (02) :421-438

[27] ALMOST AUTOMORPHIC SOLUTIONS OF SEMILINEAR STOCHASTIC HYPERBOLIC DIFFERENTIAL EQUATIONS IN INTERMEDIATE SPACE [J].

Xia, Zhinan .

KODAI MATHEMATICAL JOURNAL, 2017, 40 (03) :492-517

[28] Almost automorphic solutions for stochastic differential equations driven by fractional Brownian motion [J].

Chen, Feng ;

Yang, Xue .

MATHEMATISCHE NACHRICHTEN, 2019, 292 (05) :983-995

[29] Asymptotically almost automorphic solutions to stochastic differential equations driven by a Levy process [J].

Chang, Yong-Kui ;

Tang, Chao .

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2016, 88 (07) :980-1011

[30] Square-mean almost periodic solution for stochastic Hopfield neural networks with time-varying delays on timescales [J].

Li, Yongkun ;

Yang, Li ;

Wu, Wanqin .

NEURAL COMPUTING & APPLICATIONS, 2015, 26 (05) :1073-1084

← 1 2 3 4 5 →