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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     author = {N. T. Orumbaeva},
     title = {On solvability of non-linear semi-periodic boundary-value problem for system of hyperbolic equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {26--41},
     publisher = {mathdoc},
     number = {9},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_9_a2/}
}
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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/