The first boundary problem with an integral condition for a mixed-type equation with a characteristic degeneration

For a mixed equation of elliptic-hyperbolic type in rectangular domain the first boundary problem is investigated. The criterion of uniqueness is established. The solution of the problem is constructed in the form of the sum of a biorthogonal row. Small denominators are appeared in process of proving existence of the solution of the problem. The estimates about a remoteness from zero denominators are established with the corresponding assymptotics which allowed to prove existence of the decision in a class of regular decisions and prove its stability depending on boundary functions.