Dirichlet problem for loaded degenerating equation of the mixed type in the rectangular area

Necessary and sufficient conditions of the uniqueness of solution of the first boundary problem for the loaded degenerating equtation of Lavrentiev–Bitsadze in rectangular area are established in this work.The solution of the task is constructed in the form of the number sum on the eigen functions of a corresponding one-dimensional problem on the eigen values. The solution stability from boundary functions is showed.