Abstract
For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient matrix and the nonhomogeneous term. The obtained result confirms not only the existence, but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution. As an application, a criterion on the existence of almost periodic solutions of the second order difference equations is derived.
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References
Fink, A. M.,Almost Periodic Differential Equations, Lecture Notes in Math., Vol. 377, Berlin-New York: Springer-Verlag, 1974.
Yoshizawa, T.,Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, New York: Springer-Verlag, 1975.
Lakshmikantham, V., Trigiante, D.,Theory of Difference Equations, Numerical Methods and Applications, San Diego: Academic Press, Inc., 1988.
Elaydi, S.,An Introduction to Difference Equations, Undergraduate Texts in Mathematics, New York: Springer-Verlag, 1996.
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Zhang, S. Almost periodic solutions of difference systems. Chin.Sci.Bull. 43, 2041–2046 (1998). https://doi.org/10.1007/BF03183502
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DOI: https://doi.org/10.1007/BF03183502