On the solution of a boundary problem for a fourth order equation containing a third time derivative in semi-bounded domains

In this paper, boundary value problems in semi-bounded domains are considered for a fourth-order equation with multiple characteristics. The uniqueness of the solution is proven by the method of energy integrals. The existence of solutions is proved by the method of separation of variables. The solutions are constructed explicitly in the form of an infinite series, and the possibility of term-by-term differentiation of the series with respect to all variables is justified.