Abstract
We establish a uniqueness criterion for solution of nonlocal Dezin’s problem for an equation of mixed elliptic-hyperbolic type. The solution is constructed as a sum of a series in eigenfunctions of the corresponding one-dimensional spectral problem. In the proof of its convergence there arises a problem on small denominators arises. Under certain restrictions on the given parameters and functions we prove the convergence of constructed series in the class of regular solutions.
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Original Russian Text © K.B. Sabitov, V.A. Gushchina, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 3, pp. 37–50.
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Sabitov, K.B., Gushchina, V.A. A. A. Dezin’s problem for inhomogeneous Lavrent’ev–Bitsadze equation. Russ Math. 61, 31–43 (2017). https://doi.org/10.3103/S1066369X17030045
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DOI: https://doi.org/10.3103/S1066369X17030045