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Zaballa, Ion ; Gracia, Juan M.
On difference linear periodic systems II. Non-homogeneous case. (English). Aplikace matematiky, vol. 30 (1985), issue 6, pp. 403-412
MSC: 39A10, 39A11, 39A12, 93D05 | MR 0813529 | Zbl 0588.39001 | DOI: 10.21136/AM.1985.104170
Keywords:
reduction; explicit solution; non-homogeneous system; periodic system; asymptotic behaviour; periodic solutions
Summary:
This work deals with the reduction of a linear nonhomogeneous periodic system in differences (recurrence relations) to another linear non-homogeneous system with constant coefficients and an independent term. This makes it possible to study the existence and properties of periodic solutions, the asymptotic behavior and to obtain all solutions in closed form.
References:
[1] R. Bellman: On the boundedness of solutions of nonlinear differential and difference equations. Trans. Amer. Math. Soc. 62 (1974), no. 3, 357-386. DOI 10.1090/S0002-9947-1947-0023996-1 | MR 0023996
[2] A. Halanay D. Wexler: Qualitative Theory of Sampled-Data Systems. (Russian translation), Mir, Moscow (1971). MR 0352577
[3] I. Zaballa J. M. Gracia: On difference linear periodic systems I. Homogeneous case. Apl. mat. 28 (1983) 241-248. MR 0710173
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