Geodesic
On solvability of non-linear semi-periodic boundary-value problem for system of hyperbolic equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 26-41.

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We study a non-linear semi-periodic boundary-value problem for a system of hyperbolic equations with mixed derivative. At that, the semi-periodic boundary-value problem for a system of hyperbolic equations is reduced to an equivalent problem, consisting of a family of periodic boundary-value problems for ordinary differential equations and functional relation. When solving a family of periodic boundary-value problems of ordinary differential equations we use the method of parameterization. This approach allowed to establish sufficient conditions for the existence of an isolated solution of non-linear semi-periodic boundary-value problem for a system of hyperbolic equations.
Keywords: system of hyperbolic equations, semi-periodic boundary-value problem. 
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N. T. Orumbaeva. On solvability of non-linear semi-periodic boundary-value problem for system of hyperbolic equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 26-41. http://geodesic.mathdoc.fr/item/IVM_2016_9_a2/

[1] Cesari L., “Periodic solutions of hyperbolic partial differential equations”, Proc. Internat. Sympos. Non-linear Vibrations (Kiev, 1961), v. 2, Izd. Akad. Nauk Ukrain. SSR, Kiev, 1963, 440–457 | MR

[2] Vejvoda O., “Periodic solutions of a linear and weakly nonlinear wave equation in one dimension. I”, Czech. Math. J., 14:3 (1964), 341–382 | MR | Zbl

[3] Samoilenko A. M., Tkach B. P., Chislenno-analiticheskie metody v teorii periodicheskikh reshenii uravnenii s chastnymi proizvodnymi, Nauk. dumka, Kiev, 1992 | MR

[4] Ptashnik B. I., Nekorrektnye granichnye zadachi dlya differentsialnykh uravnenii s chastnymi proizvodnymi, Kiev, 1984 | MR

[5] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., Asimtoticheskie metody issledovaniya periodicheskikh reshenii nelineinykh giperbolicheskikh uravnenii, Nauka, M., 1998

[6] Kiguradze T. I., “O periodicheskikh kraevykh zadach dlya lineinykh giperbolicheskikh uravnenii”, Differents. uravneniya, 29:2 (1993), 281–297 | MR

[7] Zhestkov S. V., “O dvoyakoperiodicheskikh resheniyakh nelineinykh giperbolicheskikh sistem v chastnykh proizvodnykh”, Ukr. matem. zhurn., 39:4 (1987), 521–523 | MR | Zbl

[8] Mitropolskii Yu. A., Khoma G. P., Gromyak M. I., Asimptoticheskie metody issledovaniya kvazivolnovykh uravnenii giperbolicheskogo tipa, Nauk. dumka, Kiev, 1991 | MR

[9] Asanova A. T., Dzhumabaev D. S.,, “Korrektnaya razreshimost nelokalnykh kraevykh zadach dlya sistem giperbolicheskikh uravnenii”, Differents. uravneniya, 41:3 (2005), 337–346 | MR | Zbl

[10] Orumbaeva N. T., “Ob odnom algoritme nakhozhdeniya resheniya periodicheskoi kraevoi zadachi dlya sistemy kvazilineinykh giperbolicheskikh uravnenii”, Sib. elektronnye matem. izv., 10 (2013), 464–474 | MR | Zbl

[11] Dzhumabaev D. S., “Priznaki odnoznachnoi razreshimosti lineinoi kraevoi zadachi dlya obyknovennykh differentsialnykh uravnenii”, Zhurn. vychisl. matem. i matem. fiz., 29:1 (1989), 50–66 | MR | Zbl

[12] Orumbaeva N. T., Sabitbekova G., “O razreshimosti semeistva periodicheskikh kraevykh zadach dlya obyknovennykh differentsialnykh uravnenii”, Vestn. Karagandinsk. gos. un-ta. Ser. Matem., 2013, no. 4(72), 89–96

[13] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR