A problem with a shift condition on internal characteristics for one class of mixed-type equations with different orders of degeneration

In this paper, in a certain mixed-type domain for a mixed elliptic-hyperbolic equation with different orders of degeneration and with singular coefficients, theorems of uniqueness and existence of a solution to a problem with a condition of V.I. Zhegalov type and the A.M. Nakhushev condition on internal characteristics and an analogue of the F.I. Frankl condition on the degeneration segment are proved. On the boundary of the ellipticity domain, the Dirichlet condition is specified.

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