×

Asymptotically almost automorphic solutions to nonautonomous semilinear evolution equations. (English) Zbl 1241.43005

Summary: This paper is concerned with a class of nonautonomous semilinear evolution equations in Banach space. We establish an existence theorem about asymptotically almost automorphic mild solutions to the addressed evolution equation. An example is given to illustrate our abstract results.

MSC:

43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
PDFBibTeX XMLCite
Full Text: Euclid

References:

[1] P. Acquistapace and B. Terreni, A unified approach to abstract linear parabolic equations, Rend. Sem. Mat. Univ. Padova 78 (1987), 47-107. · Zbl 0646.34006
[2] P. Acquistapace, Evolution operators and strong solution of abstract linear parabolic equations, Differential Integral Equations 1 (1988), 433-457. · Zbl 0723.34046
[3] P. Cieutat, K. Ezzinbi, Existence, uniqueness and attractiveness of a pseudo almost automorphic solutions for some dissipative differential equations in Banach spaces, J. Math. Anal. Appl. 354 (2009), 494-506. · Zbl 1193.34121 · doi:10.1016/j.jmaa.2009.01.016
[4] W. A. Coppel, Dichotomies in Stability Theory , Springer-Verlag, 1978. · Zbl 0376.34001
[5] T. Diagana, Existence of pseudo-almost automorphic solutions to some abstract differential equations with \(S^p\)-pseudo-almost automorphic coefficients, Nonlinear Anal. TMA 70 (2009), 3781-3790. · Zbl 1178.43004 · doi:10.1016/j.na.2008.07.034
[6] T. Diagana, E. Hernández M, J.P.C. dos Santos, Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations, Nonlinear Anal. TMA 71 (2009), 248-257. · Zbl 1172.45002 · doi:10.1016/j.na.2008.10.046
[7] H. S. Ding, J. Liang, T. J. Xiao, Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions, J. Math. Anal. Appl. 338 (2008), 141-151. · Zbl 1142.45005 · doi:10.1016/j.jmaa.2007.05.014
[8] H. S. Ding, W. Long, G. M. N’Guérékata, A composition theorem for weighted pseudo-almost automorphic functions and applications, Nonlinear Anal. TMA 73 (2010), 2644-2650. · Zbl 1210.43008 · doi:10.1016/j.na.2010.06.042
[9] H. S. Ding, J. Liang, T. J. Xiao, Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces, Nonlinear Anal. TMA 73 (2010), 1426-1438. · Zbl 1192.43005 · doi:10.1016/j.na.2010.05.006
[10] K. Ezzinbi, S. Fatajou, G. M. N’Guérékata, Pseudo almost automorphic solutions for dissipative differential equations in Banach spaces, J. Math. Anal. Appl. 351 (2009), 765-772. · Zbl 1175.34074 · doi:10.1016/j.jmaa.2008.11.017
[11] J. Liang, J. Zhang, T.J. Xiao, Composition of pseudo almost automorphic and asymptotically almost automorphic functions, J. Math. Anal. Appl. 340 (2008), 1493-1499. · Zbl 1134.43001 · doi:10.1016/j.jmaa.2007.09.065
[12] J. Liang, G. M. N’Guérékata, T. J. Xiao, J. Zhang, Some properties of pseudo almost automorphic functions and applications to abstract differential equations, Nonlinear Anal. TMA 70 (2009), 2731-2735. · Zbl 1162.44002 · doi:10.1016/j.na.2008.03.061
[13] W. Long, Existence of positive almost automorphic solutions to a class of integral equations, Afr. Diaspora J. Math. 12 (2011), 48-56. · Zbl 1242.45006
[14] G. M. N’Guérékata, Topics in almost automorphy , Springer-Verlag, New York, 2005.
[15] G. M. N’Guérékata, A. Pankov, Stepanov-like almost automorphic functions and monotone evolution equations, Nonlinear Anal. TMA 68 (2008), 2658-2667. · Zbl 1140.34399 · doi:10.1016/j.na.2007.02.012
[16] T. J. Xiao, J. Liang, J. Zhang, Pseudo almost automorphic solution to semilinear differential equations in Banach spaces, Semigroup Forum 76 (2008), 518-524. · Zbl 1154.46023 · doi:10.1007/s00233-007-9011-y
[17] T. J. Xiao, X. X. Zhu, J. Liang, Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications, Nonlinear Anal. TMA 70 (2009), 4079-4085. · Zbl 1175.34076 · doi:10.1016/j.na.2008.08.018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.