The boundary value problem for equation of the mixed type of the third order with Gellerstedte operator in hyperbolic area

In this paper the author proves the existence and uniqueness of the solution the boundary problem for equation of the third order with multiple characteristics. The uniqueness of the solution of the problem is stated by method of energy integral. The existence of solution of the problem follows from the fact that it can be reduced to an equivalent to Fredholm integral equation of the second kind.