JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 64-71.doi: 10.6040/j.issn.1671-9352.0.2016.598

Previous Articles     Next Articles

μ-pseudo almost automorphic solutions for a class of stochastic evolution equations under non-Lipschitz conditions

RONG Wen-ping, CUI Jing*   

  1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China
  • Received:2016-12-23 Online:2017-10-20 Published:2017-10-12

PDF (PC)

434

Abstract: We establish the existence of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion under some non-Lipschitz conditions. Moreover, an example is given to illustrate our results.

Key words: stochastic evolution equation, μ-pseudo almost automorphic, fixed point theorem

CLC Number: 

  • O211.6
[1] BOCHNER S. Continuous mappings of almost automorphic and almost periodic functions[J]. Proc Natl Acad Sci USA, 1964, 52(4):907-910.
[2] ZHANG Chuanyi. Pseudo almost periodic solutions of some differential equations[J]. J Math Anal Appl, 1994, 181(1):62-76.
[3] LIANG Jin, ZHANG Jun, XIAO Tijun. Composition of pseudo almost automorphic and asymptotically almost automorphic functions[J]. J Math Anal Appl, 2008, 340(2):1493-1499.
[4] BLOT J, CIEUTAT P, EZZINBI K. New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications[J]. Appl Anal, 2013, 92(3):493-526.
[5] FU Miaomiao, LIU Zhenxin. Square-mean almost automorphic solutions for some stochastic differential equations[J]. Proc Amer Math Soc, 2010, 138(10):3689-3701.
[6] CHEN Zhang, LIN Wei. Square-mean pseudo almost automorphic process and its application to stochastic evolution equations[J]. J Funct Anal, 2011, 261(1):69-89.
[7] DIOP M A, EZZINBI K, MBAYE M M. Existence and global attractiveness of a pseudo almost periodic solution in p-th mean sense for stochastic evolution equation driven by a fractional Brownian motion[J]. Stochastics, 2015, 87(6):1061-1093.
[8] BLOT J, CIEUTAT P, EZZINBI K. Measure theory and pseudo almost automorphic functions: new developments and applications[J]. Nonlinear Anal, 2012, 75(4):2426-2447.
[9] CAO Junfei, YANG Qigui, HUANG Zaitang. On almost periodic mild solutions for stochastic functional differential equations[J]. Nonlinear Anal, 2012, 13(1):275-286.
[10] CHANG Yongkui, ZHAO Zhihan, NGuérékata G M. A new composition theorem for square-mean almost automorphic functions and applications to stochastic differential equations[J]. Nonlinear Anal, 2011, 74(6):2210-2219.
[11] LI Xiliang, HAN Yuliang, LIU Baifeng. Square-mean almost automorphic solutions to some stochastic evolution equations I: autonomous case[J]. Acta Math Appl Sin Engl Ser, 2015, 31(3):577-590.
[12] LIU Jinghuai, SONG Xiaoqiu. Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations[J]. J Funct Anal, 2010, 258(1):196-207.
[13] XIAO Tijun, LIANG Jin, ZHANG Jun. Pseudo almost automorphic solutions to semilinear differential equations in Banach space[J]. Semigroup Forum, 2008, 76(3):518-524.
[14] XIAO Tijun, ZHU Xingxing, LIANG Jin. Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications[J]. Nonlinear Anal, 2009, 70(11):4079-4085.
[15] ZHAO Zhihan, CHANG Yongkui, NIETO J J. Almost automorphic and pseudo almost automorphic mild solutions to an abstract differential equations in Banach spaces[J]. Nonlinear Anal, 2010, 72(3-4):1886-1894.
[16] EZZINBI K, MIRAOUI M. μ-pseudo almost periodic and automorphic solutions in the α-norm for some partial functional differential equations[J]. Numer Funct Anal Optim, 2015, 36(8):991-1012.
[17] CHANG Yongkui, LUO Xiaoxia. Pseudo almost automorphic behavior of solutions to a semi-linear fractional differential equation[J]. Math Commun, 2015, 20(1):53-68.
[18] CHANG Yongkui, NGuérékata G M, ZHANG Rui. Stepanov-like weighted pseudo almost automorphic functions via measure theory[J]. Bull Malays Math Sci Soc, 2016, 39(3):1005-1041.
[19] CHANG Yongkui, TANG Chao. Asymptotically almost automorphic solutions to stochastic differential equations driven by a Lévy process[J]. Stochastics, 2016, 88(7):980-1011.
[20] CAO Junfei, YANG Qigui, HUANG Zaitang. Existence and exponential stability of almost automorphic mild solutions for stochastic functional differential equations[J]. Stochastics, 2011, 83(3):259-275.
[21] SEIDLER J. Da Prato-Zabczyks maximal inequality revisited I[J]. Math Bohem, 1993, 118(1):67-106.
[1] SHEN Liu-xiao, ZHAO Chun. Optimal control for inputting rate of a size-structure competitive system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 21-29.
[2] CAO Xue-jing, LUO Zhi-xue. Optimal control of forest evolution system in polluted environment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 15-20.
[3] LI Tao-tao. Existence of radial positive solutions of second-order semi-positone elliptic differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 48-55.
[4] ZHANG Sha, JIA Mei, LI Yan, LI Xiao-chen. Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 66-72.
[5] FENG Hai-xing, ZHAI Cheng-bo. Multiple positive solutions of a system of high order nonlinear fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 48-57.
[6] CHEN Bin. Third-order periodic boundary value problems with sign-changing Greens function [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 79-83.
[7] WU Cheng-ming. Existence of positive periodic solutions for second order singular coupled systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 81-88.
[8] YANG Hao, LIU Xi-ping, WU Gui-yun. Existence of the solutions for a type of nonlocal boundary value problems for fractional differential equations with p-Laplacian operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 56-62.
[9] CHEN Qiang, JIA Mei, ZHANG Hai-bin. Existence and uniqueness of solutions for nonlinear fractional four-point boundary value problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 42-48.
[10] ZHENG Chun-hua, LIU Wen-bin. Existence of positive solutions of the boundary value problem for a class of fractional differential equations with delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 73-79.
[11] ZHAO Yu-huan, ZHANG Xiao-bin. Maximum likelihood estimation for linear stochastic evolution equations#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(05): 54-60.
[12] YANG Xue-jie, SUN Guo-zheng*, CHEN Wen. Shock solution for a quasilinear singularly perturbed problem#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 79-83.
[13] ZHOU Wen-xue1,2, LIU Hai-zhong1. Existence of solution for the  boundary value problem of a class of fractional differential equation [J]. J4, 2013, 48(8): 45-49.
[14] QIN Xiao-na, JIA Mei*, LIU Shuai. Existence of positive solutions for fractional differential equations boundary value problems with Caputo derivative [J]. J4, 2013, 48(10): 62-67.
[15] ZHANG Hai-yan1,2, LI Yao-hong2. ositive solutions of boundary value problems for systems of nonlinear mixed higher order singular differential equations [J]. J4, 2012, 47(2): 31-35.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd