Abstract
We investigate a boundary-value problem for mixed-type equation with the Lavrent’ev–Bitsadze operator in the main term and q-difference deviations of the argument in the lowest terms. We construct a general solution to the equation and prove a uniqueness theorem without restrictions on the deviation value. Then we show that the problem is uniquely solvable and find integral representations of the solution in the elliptic and hyperbolic domains.
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Original Russian Text © A.N. Zarubin, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 1, pp. 3–11.
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Zarubin, A.N. Tricomi problem for q-difference analog of anticipatory-retarding equation of mixed type. Russ Math. 61, 1–9 (2017). https://doi.org/10.3103/S1066369X17010017
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DOI: https://doi.org/10.3103/S1066369X17010017