Inverse problem for Lavrent'ev–Bitsadze equation connected with the search of elements in right-hand side

We consider an equation of mixed elliptic-hyperbolic type. Right-hand part of this equation is represented as a product of two functions, each depending on a single variable. For this equation we study an inverse problem to find unknown multiplier. We establish a criterion of the uniqueness of a solution to this problem. Solution was constructed as a sum of series on the systems of eigenfunctions. We have obtained estimates separated from zero for small denominators. The existence and stability is proved under certain conditions upon the ratio of the rectangle sides of hyperbolic part of the equation, upon the boundary functions and known multiplier in the right-hand part of equation.