Abstract
For non-homogeneous mixed parabolic-hyperbolic type equation in a rectangular area boundary-value problem is solved which was posed by in 1959 I. M. Gelfand. The solution of this problem is constructed as the sum of orthogonal series. Using the spectral analysis method, we establish a uniqueness criterion and prove the existence theorem for the solution of the problem in justifying the convergence of the problem of small denominators. In connection with this set of evaluation of separation from scratch small denominators that are allowed to prove the convergence of the class of regular solutions.
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