Third Boundary Value Problem for an Equation with the Third Order Multiple Characteristics in Three Dimensional Space

In this article, the third boundary value problem for an equation with the third order multiple characteristics in three dimensional space is studied. Uniqueness of the solution of the given problem is proved by the method of energy integral. Existence of the solution is proved by means of the method of variables separation. The solution is constructed in the exact infinite series form and an opportunity of term-by-term differentiation is justified. It is important in smooth convergence of the series, that ''small denominator'' is different from zero.