ИСТИНА

A mixed boundary value problem with the oblique derivative for the Lavrentiev-Bitsadze equation with the spectral parameter may be reduced to a problem for the Helmholtz equation in a semi-disk. To explore it, we start from a problem with the Dirichlet boundary condition on the diameter. The problem is reduced to a singular integral equation with floating factors which may be solved explicitly. This work was partially supported by the Russian Foundation for Basic Research under grants no. 17-01-00847a and 17-51-18042 Bolg_a. References: 1. Il’in, V.A. and Moiseev, E.I., On the Absence of the Basis Property of a System of Root Functions of a Problem with an Oblique Derivative, Differ. Uravn., 1994, vol. 30, no. 1, pp. 128–143. 2. Moiseev, E.I., Disposition of the Spectrum of a Boundary Value Problem with Mixed Boundary Conditions, Differ. Uravn., 1988, vol. 24, no. 1, pp. 123–135. 3. Moiseev, E.I., Disposition of the Spectrum of the Tricomi Problem for the Lavrent’ev-Bitsadze Equation, Differ. Uravn., 1989, vol. 25, no. 1, pp. 97–106. 4. Polosin, A.A., On the Location of the Spectrum of a Mixed Boundary Value Problem for the Laplace Equation in a Half-Disk, Differ. Uravn., 2006, vol. 42, no. 5, pp. 684–697.