Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients

References

[1] ACQUISTAPACE, P.: Evolution operators and strong solutions of abstract linear parabolic equations, Differential Integral Equations 1 (1988), 433-457.10.57262/die/1372451947Search in Google Scholar

[2] ACQUISTAPACE, P.-TERRENI, B.: A unified approach to abstract linear nonautonomous parabolic equations, Rend. Semin. Mat. Univ. Padova 78 (1987), 47-107.Search in Google Scholar

[3] ADAMCZAK, A.: Cn-almost periodic functions, Comment. Math. (Prace Mat.) 37 (1997), 1-12.Search in Google Scholar

[4] ADAMCZAK, M.-STOÍNSKI, S.: On the (NC(n))-almost periodic functions. In: Proceedings of the 6th. Conference on Functions Spaces (R. Grz¸aślewicz, Cz. Ryll-Nardzewski, H. Hudzik, J. Musielak, eds.), World Scientific Publishing, River Edge, NJ, 2003, pp. 39-48.Search in Google Scholar

[5] AL-ISLAM, N. S.-ALSULAMI, S.-DIAGANA, T.: Existence of weighted pseudo antiperiodic solutions to some non-autonomous differential equations, Appl. Math. Comput. 218 (2012), 6536-6548.10.1016/j.amc.2011.12.026Search in Google Scholar

[6] AMANN, H.: Linear and Quasilinear Parabolic Problems, Birkh¨auser, Berlin, 1995.10.1007/978-3-0348-9221-6Search in Google Scholar

[7] BAILLON, J. B.-BLOT, J.-NGUÉR´ EKATA, G. M.-PENNEQUIN, D.: On C(n)-almost periodic solutions to some nonautonomous differential equations in Banach spaces, Comment. Math. (Prace Mat.) 46 (2006), 263-273.Search in Google Scholar

[8] BAROUN, M.-BOULITE, S.-DIAGANA, T.-MANIAR, L.: Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations, J. Math. Anal. Appl. 349 (2009), 74-84.10.1016/j.jmaa.2008.08.034Search in Google Scholar

[9] BUGAJEWSKI, D.-NGUÉRÉKATA, G. M.: On some classes of almost periodic functions in abstract spaces, Int. J. Math. Math. Sci. 61 (2004), 3237-3247.10.1155/S016117120440653XSearch in Google Scholar

[10] CHICONE, C.-LATUSHKIN, Y.: Evolution Semigroups in Dynamical Systems and Differential Equations. Math. Surveys Monogr. 70, Amer. Math. Soc., Providence, RI, 1999.10.1090/surv/070Search in Google Scholar

[11] DIAGANA, T.-NELSON, V.: C(n)-Pseudo almost automorphy and its applications to some higher-order differential equations, Nonlinear Stud. 19 (2012), 443-455.Search in Google Scholar

[12] DIAGANA, T.: Almost periodic solutions for some higher-order nonautonomous differential equations with operator coefficients, Math. Comput. Modelling 54 (2011), 2672-2685.10.1016/j.mcm.2011.06.050Search in Google Scholar

[13] DIAGANA, T.: Weighted pseudo-almost periodic functions and applications, C. R. Acad. Sci. Paris, Ser. I 343 (2006), 643-646.Search in Google Scholar

[14] DIAGANA, T.: Almost periodic solutions to some second-order nonautonomous differential equations, Proc. Amer. Math. Soc. 140 (2012), 279-289.10.1090/S0002-9939-2011-10970-5Search in Google Scholar

[15] ELAZZOUZI, A.: C(n)-almost periodic and C(n)-almost automorphic solutions for a class of partial functional differential equations with finite delay, Nonlinear Anal. Hybrid Syst. 4 (2010), 672-688.10.1016/j.nahs.2010.04.005Search in Google Scholar

[16] ENGEL, K. J.-NAGEL, R.: One Parameter Semigroups for Linear Evolution Equations. Grad. Texts in Math., Springer Verlag, Berlin, 1999.Search in Google Scholar

[17] EZZINBI, K.-NELSON, N.-N’GUÉRÉKATA, G. M.: C(n)-almost automorphic solutions of some nonautonomous differential equations, Cubo 10 (2008), 61-74.Search in Google Scholar

[18] EZZINBI, K.-FATAJOU, S.-NGUÉRÉKATA, G. M.: Massera type theorem for the existence of C(n)-almost periodic solutions for partial functional differential equations with infinite delay, Nonlinear Anal. 69 (2008), 1413-1424.10.1016/j.na.2007.06.041Search in Google Scholar

[19] EZZINBI, K.-FATAJOU, S.-N’GUÉRÉKATA, G. M.: C(n)-almost automorphic solutions for partial neutral functional differential equations, Appl. Anal. 86 (2007), 1127-1146.10.1080/00036810701584591Search in Google Scholar

[20] LIANG, J.-MANIAR, L.-N’GUÉRÉKATA, G. M.-XIAO, T. J.: Existence and uniqueness of C(n)-almost periodic solutions to some ordinary differential equations, Nonlinear Anal. 66 (2007), 1899-1910.10.1016/j.na.2006.02.030Search in Google Scholar

[21] LIU, Y.: Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695-720.10.2478/s12175-012-0039-4Search in Google Scholar

[22] LIANG, J.-N’GUÉR´ EKATA, G. M.-XIAO, T. J.-ZHANG J.: Some properties of pseudo almost automorphicfunctions and applications to abstract differential equations, Nonlinear Anal. 70 (2009), 2731-2735.10.1016/j.na.2008.03.061Search in Google Scholar

[23] LIANG, J.-XIAO, T. J.-ZHANG J.: Decomposition of weighted pseudo-almost periodic functions, Nonlinear Anal. 73 (2010), 3456-3461.10.1016/j.na.2010.07.034Search in Google Scholar

[24] LUNARDI, A.: Analytic Semigroups and Optimal Regularity in Parabolic Problems. Progr. Nonlinear Differential Equations Appl. 16, Birkh¨auser Verlag, Basel, 1995.10.1007/978-3-0348-9234-6Search in Google Scholar

[25] SCHNAUBELT, R.: Parabolic evolution equations with asymptotically autonomous delay, Trans. Amer. Math. Soc. 356 (2004), 3517-3543.10.1090/S0002-9947-03-03512-8Search in Google Scholar

[26] XIAO, T. J.-ZHU, X. X.-LIANG, J.: Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications, Nonlinear Anal. 70 (2009), 4079-4085.10.1016/j.na.2008.08.018Search in Google Scholar

[27] XIAO, T. J.-LIANG, J.-ZHANG, J.: Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces, Semigroup Forum 76 (2008), 518-524.10.1007/s00233-007-9011-ySearch in Google Scholar

[28] XIAO, T. J.-LIANG, J.: The Cauchy Problem for Higher-Order Abstract Differential Equations. Lecture Notes in Math. 1701, Springer, Berlin, 1998.Search in Google Scholar

[29] ZHANG, X.-TANG, X.: Non-constant periodic solutions for second order Hamiltonian system with a p-Laplacian, Math. Slovaca 62 (2012), 231-246. 10.2478/s12175-012-0005-1Search in Google Scholar