A uniqueness criterion for solutions of the Dirichlet problem for a loaded equation with the Lavrent'ev-Bitsadze operator

The first boundary value problem was considered for the second order loaded differential equation of mixed elliptic-hyperbolic type in a rectangular region. The local and nonlocal problems for the loaded partial differential equations of the individual and mixed types have been previously studied in areas where the hyperbolic part is the characteristic triangle. In this work, in contrast to the well-known ones, necessary and sufficient conditions of the uniqueness of this problem solution were found by the method of spectral analysis.