Geodesic
Boundary value problems for a~hyperbolic equation with nonlocal conditions of the~I and II~kind
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 74-83

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In this paper we consider two initial-boundary value problems with nonlocal conditions. The main goal is to propose a method for proving the solvability of nonlocal problems with integral conditions of the first kind. The proposed method is based on the equivalence of a nonlocal problem with an integral condition of the first kind and a nonlocal problem with an integral condition of the second kind in a special form. We prove the unique existence of generalized solutions to both problems.
Keywords: hyperbolic equation, nonlocal problem, integral conditions, generalized solution. 
@article{IVM_2012_4_a7,
     author = {L. S. Pul'kina},
     title = {Boundary value problems for a~hyperbolic equation with nonlocal conditions of {the~I} and {II~kind}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {74--83},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_4_a7/}
}
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L. S. Pul'kina. Boundary value problems for a~hyperbolic equation with nonlocal conditions of the~I and II~kind. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 74-83. http://geodesic.mathdoc.fr/item/IVM_2012_4_a7/