Nonlocal inverse problem to find unknown multipliers in right part of Lavrentev–Bitsadze equation

We consider the equation of mixed elliptic-hyperbolic type. Right part of this equation is represented as a product of two functions, each of a single variable. We study an inverse problem for this equation to find unknown multipliers. We establish a criterion of the uniqueness of a solution to this problem. Solution was constructed as a sums of series on the systems of eigenfunctions corresponding one-dimensional spectral problem. We have obtained estimates bounded away 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 boundary functions and known multipliers in the right parts of equation.