Geodesic
Tricomi problem for $q$-difference analog of anticipatory-retarding equation of mixed type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 3-11

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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. 
@article{IVM_2017_1_a0,
     author = {A. N. Zarubin},
     title = {Tricomi problem for $q$-difference analog of anticipatory-retarding equation of mixed type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--11},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_1_a0/}
}
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A. N. Zarubin. Tricomi problem for $q$-difference analog of anticipatory-retarding equation of mixed type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 3-11. http://geodesic.mathdoc.fr/item/IVM_2017_1_a0/