On Constructing a Solution to a Boundary Value Problem for a Third-Order Inhomogeneous Equation Using the Green’s Function in Three-Dimensional Space

In this paper, a boundary value problem for a third-order non-homogeneous equation with multiple characteristics in three-dimensional space is considered. The uniqueness of the solution to the problem is proven by the method of energy integrals. The existence of a solution is proven by the method of separation of variables. The solution is written out through the constructed Green 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.

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