Third boundary value problem for a third-order inhomogeneous equation with multiple characteristics in three-dimensional space

Abstract. In this paper, the third boundary value problem for a third-order nonhomogeneous equation with multiple characteristics in three-dimensional space is considered. The uniqueness of the solution to the problem is proved by the method of energy integrals, and its existence is proved by the method of separation of variables. The solution is presented in the form of a constructed Green’s function. Conditions for the given functions that ensure the regularity of the solution to the problem are found. When substantiating uniform convergence, a difference from zero of the "small denominator" is established.