Abstract
For a linear system of hyperbolic equations of the second order with two independent variables, we investigate the problem of the existence and uniqueness of a solution periodic in both variables and a solution periodic in one of the variables and bounded on a plane. By using the method of introduction of functional parameters, we obtain sufficient conditions for the unique solvability of the problems under consideration.
REFERENCES
L. Cesari (1963) Periodic solutions of partial differential equations Proceedings of the International Symposium on Nonlinear Oscillations Ukrainian Academy of Sciences Kiev 440–457
A. K. Aziz (1966) ArticleTitlePeriodic solutions of hyperbolic partial differential equations Proc. Amer. Math. Soc. 17 IssueID3 557–566
O. Vejvoda et al. (1982) Partial Differential Equations: Time-Periodic Solutions M. Nijhoff The Hague
B. I. Ptashnik (1984) Ill-Posed Boundary-Value Problems for Partial Differential Equations Naukova Dumka Kiev
Yu. A. Mitropol’skii G. P. Khoma M. I. Gromyak (1991) Asymptotic Methods for the Investigation of Quasiwave Equations of Hyperbolic Type Naukova Dumka Kiev
T. I. Kiguradze (1998) ArticleTitleOn doubly periodic solutions of one class of nonlinear hyperbolic equations Differents. Uravn. 34 IssueID2 238–245
D. S. Dzhumabaev (1989) ArticleTitleCriteria for the unique solvability of a linear boundary-value problem for an ordinary differential equation Zh. Vychisl. Mat. Mat. Fiz. 29 IssueID1 50–66
D. S. Dzhumabaev A. T. Asanova (2001) ArticleTitleMethod of parametrization applied to a semi-periodic boundary-value problem for a hyperbolic equation Izv. MON RK, NAN RK, Ser. Fiz.-Mat. 1 23–29
D. S. Dzhumabaev (1990) ArticleTitleApproximation of a bounded solution of a linear ordinary differential equation by solutions of two-point boundary-value problems Zh. Vychisl. Mat. Mat. Fiz. 30 IssueID3 388–404
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 562–572, April, 2004.
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Asanova, A.T., Dzhumabaev, D.S. Periodic solutions of systems of hyperbolic equations bounded on a plane. Ukr Math J 56, 682–694 (2004). https://doi.org/10.1007/s11253-005-0103-0
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DOI: https://doi.org/10.1007/s11253-005-0103-0