The first boundary value problem for a degenerate hyperbolic equation

Under certain hypothesis on the coefficients the condition is found for unique solvability of the first boundary value problem for a degenerate hyperbolic equation in the region. The uniqueness of the solution of the problem is proved by Tricomi method and existence by the method of integral equations. The solutions obtained with respect to the traces of the sought solution of integral equations are found and written out explicitly. It is shown that whenever the hypothesis of the theorem is violated, then the homogeneous problem corresponding to the problem under study has an infinite number of linearly independent solutions.