  In this article the correctness of al inear inverse problem with
semi-nonlocal boundary conditions for a three-dimensional equation in a
parallelepiped is considered. The equation itself is a fourth order mixed type
equation of the second kind. The existence and uniqueness theorems for a
generalized solution of the inverse problem in a certain class of integrable
functions are~proved using the methods of Fourier, "$\varepsilon
$-regularization", a priori estimates, approximating sequences and contracting
mappings.
