Tricomi problem for $q$-difference analog of anticipatory-retarding equation of mixed type

A. N. Zarubin

Orel State University, 95 Komsomol'skaya str., Orel, 302026 Russia

Abstract: We investigate a boundary-value problem for mixed-type equation with the Lavrent'ev–Bitsadze operator in the main part and $q$-difference deviations of an argument in the lowest terms. We construct a general solution to the equation and prove a uniqueness theorem without limitations on the deviation value. The problem is solvable. We find integral representations of solutions in the elliptic and hyperbolic domains.

Keywords: mixed-type equation, integral equation, $q$-difference equation, successive approximations method.

UDC: 517.956

Received: 01.07.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:1, 1–9

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