Geodesic
The problem in the unbounded domain with the Frankl condition on the segment of the degeneration line and with the missing Gellerstedt condition for a class of mixed-type equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2023), pp. 35-44

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In an unbounded domain, for a class of equations of mixed type with a singular coefficient, the correctness of the problem is investigated when one of the internal characteristics is freed from the Gellerstedt condition and this missing local condition is replaced by an analogue of the Frankl condition on the degeneration line. The uniqueness of the solution of the problem posed is proved using the extremum principle, and the existence of a solution to the problem is proved by the method of integral equations.
Keywords: mixed type equations with a singular coefficient, unbounded mixed domain, missing Gellerstedt condition, analogue of the Frankl condition, nonstandard singular integral equation, isolated first-order singularity. 
@article{IVM_2023_8_a3,
     author = {M. Mirsaburov and S. B. Ergasheva},
     title = {The problem in the unbounded domain with the {Frankl} condition on the segment of the degeneration line and with the missing {Gellerstedt} condition for a class of mixed-type equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {35--44},
     publisher = {mathdoc},
     number = {8},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_8_a3/}
}
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M. Mirsaburov; S. B. Ergasheva. The problem in the unbounded domain with the Frankl condition on the segment of the degeneration line and with the missing Gellerstedt condition for a class of mixed-type equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2023), pp. 35-44. http://geodesic.mathdoc.fr/item/IVM_2023_8_a3/