A problem with a missing displacement condition for one class of mixed-type equations with different orders of degeneration

In a certain mixed domain, uniqueness and existence theorems are established for a mixed elliptic-hyperbolic equation with singular coefficients and different orders of degeneration. The problem involves a boundary condition of the V. I. Zhegalov–A. M. Nakhushev type on parts of the characteristic boundary and an analogue of the F. I. Frankl condition on the degeneration segment. On the boundary of the ellipticity domain, the Dirichlet condition is specified.

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