On one boundary value problem for the Gellerstedt equation with a singular coefficient

M. Kh. Ruziev, N. T. Yuldasheva

V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 81 M. Ulugbek Ave., Tashkent, 100170 Republic of Uzbekistan

Abstract: A problem with the Bitsadze–Samarskii and Frankl conditions for a mixed-type equation in a domain whose elliptic part is the first quadrant of the plane, and the hyperbolic part is the characteristic triangle is studied. The correctness of the formulated problem is proved.

Keywords: extremum principle, uniqueness of solution, existence of solution, singular integral equation, Wiener–Hopf equation, index of equation.

UDC: 517.956

Received: 18.01.2024
Revised: 18.01.2024
Accepted: 20.03.2024

DOI: 10.26907/0021-3446-2024-12-57-70

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2024, 68:12, 57–69