Geodesic
A.A.~Dezin's problem for inhomogeneous Lavrent'ev--Bitsadze equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2017), pp. 37-50

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We establish a criterion for the uniqueness of a solution to nonlocal Dezin's problem for an equation of mixed elliptic-hyperbolic type. The solution is constructed in the form of a sum of a series in eigenfunctions of the corresponding one-dimensional spectral problem. In substantiation of the convergence of series a problem of small denominators arizes. Under certain specified conditions with respect to given pagameters and functions we prove the convergence of constructed series in a class of regular solutions.
Keywords: inhomogeneous equation of mixed type, nonlocal problem, inhomogeneous boundary condition, spectral method, uniqueness, series.
Mots-clés : existence 
@article{IVM_2017_3_a3,
     author = {K. B. Sabitov and V. A. Gushchina (Novikova)},
     title = {A.A.~Dezin's problem for inhomogeneous {Lavrent'ev--Bitsadze} equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {37--50},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_3_a3/}
}
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K. B. Sabitov; V. A. Gushchina (Novikova). A.A.~Dezin's problem for inhomogeneous Lavrent'ev--Bitsadze equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2017), pp. 37-50. http://geodesic.mathdoc.fr/item/IVM_2017_3_a3/