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The existence of almost periodic solutions of a certain nonlinear system. (English) Zbl 1221.34118
Summary: This paper studies a certain nonlinear system. By averaging method and exponential dichotomy, some sufficient conditions are given for the existence of almost periodic solutions of the system. The results generalize the known ones.

34C27Almost and pseudo-almost periodic solutions of ODE
34C29Averaging method
Full Text: DOI
[1] Seifert, G.: On almost periodic solutions for undamped systems with almost periodic forcing, Proc am math soc 31, No. 1, 104-108 (1972) · Zbl 0235.34101 · doi:10.2307/2038521
[2] Chongyou, He: On almost periodic solutions for nonlinear systems with almost periodic forcing, Ann differ eqs 4, 403-420 (1987) · Zbl 0647.34039
[3] Seifert, G.: Almost periodic solution by the method of averaging, Lecture note in mathematics 243, 123-133 (1973) · Zbl 0228.34024
[4] Fink, A. M.: Almost periodic differential equations, Lecture notes in mathematics 337 (1974) · Zbl 0325.34039
[5] Chongyou, He: Almost periodic differential equations, (1992)
[6] Copple, W. A.: Dichotomies in stability theory, Lecture notes in mathematics 629 (1978)
[7] Hale, J. K.: Ordingary differential equations, (1969) · Zbl 0186.40901
[8] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[9] Gopalsamy, K.: Stability and oscillation in delay differential equations of population dynamics, Mathematics and its applications 74 (1992) · Zbl 0752.34039
[10] He, C. Y.: Existence of almost periodic solutions of perturbation systems, Ann differ eqs 9, No. 2, 173-181 (1993) · Zbl 0778.34032
[11] Lin, M. R.: The existence of almost periodic solution and bounded solution of perturbation systems, Acta math appl sinica 22A, No. 1, 61-70 (2002) · Zbl 1006.34037
[12] Xia, Y. H.; Han, M.: New conditions on the existence and stability of periodic solution in Lotka -- Volterra’s population system, SIAM J appl math 69, No. 6, 1580-1597 (2009) · Zbl 1181.92084 · doi:10.1137/070702485
[13] Xia, Y. H.; Lin, M. R.; Cao, J.: The existence of almost periodic solutions and bounded solutions of certain perturbation systems, J math anal appl 310, No. 1, 81-96 (2005) · Zbl 1089.34039 · doi:10.1016/j.jmaa.2005.01.046
[14] Lin, Z.: The existence of almost periodic solutions of linear system, Acta math sinica 22, No. 5, 515-528 (1979) · Zbl 0432.34025
[15] Jiang, D.: Almost periodic solutions of the mathics equation with almost periodic forcing, J Nanjing univ. (Natural science edition) 21, No. 3, 417-420 (1985) · Zbl 0615.34039
[16] Xia, Y. H.; Cheng, S. S.: Quasi-uniformly asymptotic stability and existence of almost periodic solutions of difference equations with applications in population dynamic systems, J differ eqs appl 14, No. 1, 59-81 (2008) · Zbl 1141.39012 · doi:10.1080/10236190701470407
[17] Xia, Y. H.; Yang, Z.; Han, M.: Synchronization schemes for coupled identical Yang -- Yang type fuzzy cellular neural networks, Commun nonlinear sci numer simul 14, No. 9 -- 10, 3645-3659 (2009) · Zbl 1221.37227 · doi:10.1016/j.cnsns.2009.01.028
[18] Yuan, R.; Hong, J.: The existence of almost periodic solutions for a class of differential equations with piecewise constant argument, Nonlinear anal TWA 8, 1439-1450 (1997) · Zbl 0869.34038 · doi:10.1016/0362-546X(95)00225-K
[19] Yuan, R.: The existence of almost periodic solutions of retarded differential equations with piecewise constant argument, Nonlinear anal 7, 1013-1032 (2002) · Zbl 1015.34058 · doi:10.1016/S0362-546X(00)00231-5
[20] Yuan, R.: Almost periodic solution of a class of semilinear wave equations with boundary dissipation, Nonlinear anal 50, 746-761 (2002) · Zbl 1001.35008 · doi:10.1016/S0362-546X(01)00783-0
[21] Frddeman, H. I.: Deterministic mathematical models in population, ecology, (1980)
[22] Huang, Z. K.; Mohamod, S.; Bin, H.: Multiperiodicity analysis and numerical simulation of discrete-time transiently chaotic non-autonomous neural networks with time-varying delays, Commun nonlinear sci numer simul 15, No. 5, 1348-1357 (2010) · Zbl 1221.37187 · doi:10.1016/j.cnsns.2009.05.060
[23] Sun, D. X.: A note for a second order periodic linear differential equation, Commun nonl sci numer simul 15, 3339-3348 (2010) · Zbl 1222.34065 · doi:10.1016/j.cnsns.2010.01.006
[24] Ding, W.; Xing, Y. P.: Anti-periodic boundary value problems for first order impulsive functional differential equations, Applied math comput 186, No. 1, 45-53 (2007) · Zbl 1124.34039 · doi:10.1016/j.amc.2006.07.087
[25] Li, X. D.: Uniform asymptotic stability and global stability of impulsive infinite delay differential equations, Nonlinear anal 70, 1975-1983 (2009) · Zbl 1175.34094 · doi:10.1016/j.na.2008.02.096
[26] Kuang, Y.: Delay differential equations with application dynamic, (1988)