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Existence of pseudo-almost automorphic solutions for nonlinear differential equations. (English) Zbl 1312.43005
The concept of pseudo-almost automorphic functions, which is an extension of almost automorphy, has been investigated by many mathematicians. By using the Leray-Schauder fixed point theorem the authors studies the existence of pseudo-almost automorphic solutions to linear differential equations which have an exponential trichotomy.
MSC:
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
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[1] Bochner, S, Continuous mappings of almost automorpic and almost periodic functions, Proc. Natl. Acad. Sci. USA, 52, 907-910, (1964) · Zbl 0134.30102
[2] Bohr, H. Almost periodic functions. Chelsea Publishing Company, New York, 1947 · Zbl 0005.20303
[3] Bugajewski, D; N’Guérékata, GM, On the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces, Nonlinear Anal., 59, 1333-1345, (2004) · Zbl 1071.34055
[4] Bugajewski, D; Diagana, T; Mahop, CM, Asymptotic and pseudo almost periodicity of convolution operator and applications to differential and integral equations, Z. Anal. Anwendungen, 25, 327-340, (2006) · Zbl 1107.44002
[5] Diagana, T, Existence of \(p\)-almost automorphic mild solution to some abstract differential equations, Int. J. Evol. Equ., 1, 7-67, (2005) · Zbl 1083.35052
[6] Ding, HS; Liang, J; Xiao, TJ, Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces, Non. Anal., 73, 1426-1438, (2010) · Zbl 1192.43005
[7] Elaydi, S; Hajek, O, Exponential trichotomy of differential systems, J. Math. Anal. Appl., 129, 362-374, (1988) · Zbl 0651.34052
[8] Goldstein, JA; N’Guérékata, GM, Almost automorphic solutions of semilinear evolution equations, Proc. Amer. Math. Soc., 133, 2401-2408, (2005) · Zbl 1073.34073
[9] Hong, JL; Obaya, R; Gil, AS, Exponential trichotomy and a class of ergodic solutions of differential equations with ergodic perturbations, Appl. Math. L., 12, 7-13, (1999) · Zbl 0935.34044
[10] Liang, J; Zhang, J; Xiao, TJ, Composition of pseudo almost automorphic functions, J. Math. Anal. Appl., 340, 1493-1499, (2008) · Zbl 1134.43001
[11] Liang, J; N’Guérékata, GM; Xiao, TJ; Zhang, J, Some properties of pseudo-almost automorphic functions and applications to abstract differential equations, Non. Anal., 70, 2731-2735, (2009) · Zbl 1162.44002
[12] N’Guérékata, GM, Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations, Semigroup Forum, 69, 80-86, (2004) · Zbl 1077.47058
[13] N’Guérékata, G.M. Topics in Almost Automorphy. Springer-Verlag, New York, Boston, Dordrecht, London, Moscow, 2005 · Zbl 1073.43004
[14] Xiao, TJ; Liang, J; Zhang, J, Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces, Semigroup Forum, 76, 518-524, (2008) · Zbl 1154.46023
[15] Xiao, TJ; Zhu, XX; Liang, J, Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications, Non. Anal., 70, 4079-4085, (2009) · Zbl 1175.34076
[16] Zhao, ZH; Chang, YK; N’Guérékata, GM, Pseudo-almost automorphic mild solutions to semilinear integral equations in a Banach space, Non. Anal., 74, 2887-2894, (2011) · Zbl 1298.45018
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