Existence and stability of μ-pseudo almost automorphic solutions for stochastic evolution equations

作者: Jing Cui , Wenping Rong

DOI: 10.1007/S11464-019-0754-Z

关键词:

摘要: We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on functional space such like completeness composition theorems. Under conditions, we establish existence, uniqueness, global exponentially stability mild solutions for class nonlinear stochastic evolution equations driven Brownian motion separable Hilbert space.

参考文章(31)
ChuanYi Zhang, FengLin Yang, Pseudo almost periodic solutions to parabolic boundary value inverse problems Science in China Series A: Mathematics. ,vol. 51, pp. 1203- 1214 ,(2008) , 10.1007/S11425-008-0006-2
Jing-huai Liu, Xiao-qiu Song, Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations Journal of Functional Analysis. ,vol. 258, pp. 196- 207 ,(2010) , 10.1016/J.JFA.2009.06.007
Jin Liang, Jun Zhang, Ti-Jun Xiao, Composition of pseudo almost automorphic and asymptotically almost automorphic functions Journal of Mathematical Analysis and Applications. ,vol. 340, pp. 1493- 1499 ,(2008) , 10.1016/J.JMAA.2007.09.065
Joël Blot, Philippe Cieutat, Khalil Ezzinbi, Measure theory and pseudo almost automorphic functions: New developments and applications Nonlinear Analysis-theory Methods & Applications. ,vol. 75, pp. 2426- 2447 ,(2012) , 10.1016/J.NA.2011.10.041
G. Da Prato, Constantin Tudor, Periodic and almost periodic solutions for semilinear stochastic equations Stochastic Analysis and Applications. ,vol. 13, pp. 13- 33 ,(1995) , 10.1080/07362999508809380
Ti-Jun Xiao, Jin Liang, Jun Zhang, Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces Semigroup Forum. ,vol. 76, pp. 518- 524 ,(2008) , 10.1007/S00233-007-9011-Y
Mamadou Abdoul Diop, Khalil Ezzinbi, Mamadou Moustapha Mbaye, 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 Stochastics An International Journal of Probability and Stochastic Processes. ,vol. 87, pp. 1061- 1093 ,(2015) , 10.1080/17442508.2015.1026345
S. Bochner, CONTINUOUS MAPPINGS OF ALMOST AUTOMORPHIC AND ALMOST PERIODIC FUNCTIONS Proceedings of the National Academy of Sciences of the United States of America. ,vol. 52, pp. 907- 910 ,(1964) , 10.1073/PNAS.52.4.907
Zhang Chen, Wei Lin, Square-mean pseudo almost automorphic process and its application to stochastic evolution equations Journal of Functional Analysis. ,vol. 261, pp. 69- 89 ,(2011) , 10.1016/J.JFA.2011.03.005