The Dirichlet problem for a mixed-type equation in a rectangular domain (Q5942106)

For the equation with degree degeneration \[ \operatorname {sgn}y\cdot|y|^m u_{xx}+ u_{yy}- \lambda^2 \operatorname {sgn}y\cdot|y|^m= 0, \quad \lambda\in \mathbb{R} \] in the mixed rectangular domain \(D\), sufficient conditions of a solvability and criterion of uniqueness of a solution of the Dirichlet problem are proposed. The solution of the problem is constructed by a method of a separation of variables.