Nonlocal problem for a mixed type fourth order differential equation in three dimensional domain

This article considers solvability of nonlocal mixed-value problem for a three-dimensional homogeneous mixed-type fourth-order differential equation. Solution construction for such equation is examined, too. Spectral method based on separation of variables is used in the article. The criterion of one-value solvability of the problem considered is installed. Under this criterion one-valued solvability of the problem is proved.