Existence of almost periodic solutions for neutral delay difference systems
Tóm tắt
In this paper, the existence of almost periodic solutions is studied via the Lyapunov function. Razumikhin type theorems are established on the existence, uniqueness and uniformly asymptotic stability of almost periodic solutions. Two examples are given to explain our results.
Tài liệu tham khảo
Agarwal R P. Difference Equations and Inequalities. 2nd Ed. New York: Dekker, 2000
Cooke K L. Stability analysis for a vector disease model. Rocky Mountain J Math, 1977, 9: 31–42
Corduneanu C. Almost Periodic Functions. New York: Chelsea, 1989
Fink A M, Seifert G. Liapunov functions and almost periodic solutions for almost periodic systems. J Diff Eqns, 2969, 5: 307–313
Gopalsamy K, Mohamad S. Canonical solutions and almost periodicity in a discrete logistic equation. Appl Math Comput, 2000, 113(2–3): 305–323
Hale J K. Periodic and almost periodic solution of functional differential equations. Arch Rational Mech Anal, 1964, 15: 289–309
Hale J K. Theory of Functional Differential Equations. Berlin: Springer, 1977
Hamaya Y. Existence of an almost periodic solution in a difference equation by Liapunov functions. Nonlinear Studies, 2001, 8(3): 373–379
Hino Y. Almost periodic solutions of functional differential equations with infinite retardation. II. Tohoku Math J, 1980, 32: 525–530
Lakshmikantham V, Trigiante D. Theory of Difference Equations. New York: Academic Press, INC, 1988
Meisters G H. On almost periodic solutions of a class of differential equations. Proc Amer Math Soc, 1959, 10: 113–119
Nakajima F. Existence of almost periodic solutions by Liapunov functions. Tohoku Math J, 1975, 27: 69–74
Sawano K. Exponential asymptotic stability for functional-differential equations with infinite retardations. Tohoku Math J, 1979, 31: 363–382
Yang X, Yuan R. On the module and spectral of almost periodic sequence in Banach space. J Beijing Normal University, 2005, 41(5): 455–459
Yoshizawa T. Extreme stability and almost periodic solutions of functional-differential equations. Arch Rational Mech Anal, 1964, 17: 148–170
Yoshizawa T. Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions. Applied Mathematical Sciences, Vol 14. Berlin: Springer-Verlag, 1975
Yuan R. Existence of almost periodic solution of functional differential equations. Ann of Diff Eqs, 1991, 7(2): 234–242
Yuan R. Existence of almost periodic solutions of functional differential equations of neutral type. J Math Anal Appl, 1992, 165(2): 524–538
Yuan R. Existence of almost periodic solutions of neutral functional-differential equations via Liapunov-Razumikhin function. Z Angew Math Phys, 1998, 49: 113–136
Yuan R. The existence of almost periodic solutions of retarded differential equations with piecewise constant argument. Nonlinear Anal, 2002, 48: 1013–1032
Yuan R, Hong J L. The existence of almost periodic solutions for a class of differential equations with piecewise constant argument. Nonlinear Analysis TMA, 1997, 28(8): 1439–1450
Zhang S. Existence of almost periodic solutions for differences systems. Ann of Diff Eqs, 2000, 16(2): 184–206
Zhang S, Liu P, Gopalsamy K. Almost periodic solutions of nonautonomous linear difference equations. Appl Anal, 2002, 81(2): 281–301
Zheng G, Zhang S. Existence of almost periodic solutions of neutral delay difference systems. Dynamics of Continuous, Discrete and Impulsive Systems, Ser A: Math Anal, 2002, 9: 523–540