Boundary problems in a special domain for an equation of mixed type

Boundary value problems for a mixed type equation with a spectral parameter in a region consisting of two sectors of a circle and two characteristic triangles are formulated; the unique solvability of the problems posed is proved. The objects of study are boundary value problems for differential equations of mixed type with a spectral parameter. The purpose of the study is the formulation and study of boundary value problems for differential equations of mixed type with a spectral parameter in special domains. Methods of the theory of partial differential equations and the theory of singular integral equations, energy integrals, and the principle of extremum, as well as the method of separation of variables and the theory of Bessel functions, were used. The results include the formulation of boundary-value problems for a mixed type equation with the spectral parameter in a region consisting of two sectors of a circle and two characteristic triangles. It has been proved that the problems are uniquely solvable.