Problem with Combined Local and Nonlocal Conditions on One Boundary Characteristic for One Class of Equations of Mixed Type

In this paper, in a certain finite mixed domain for the equation $$(\textrm{sign}\,y)|y|^{m}u_{xx}+u_{yy}-\frac{m}{2y}u_{y}=0$$ the problem with combined Tricomi conditions and an analogue of the Frankl condition on one boundary characteristic is studied. The uniqueness of the solution of the problem is proved using the extreme principle of A.V. Bitsadze. The existence of a solution to the problem is proved using the theory of singular integral equations, Wiener–Hopf equations, and Fredholm equations of the second kind.

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