General boundary value problem for the third order linear differential equation of composite type

The boundary value problem is considered for the linear two-dimensional integro-differential loaded third order equation of composite type with non-local terms in the boundary conditions. The principal part of the equation is a derivative of the two-dimensional Laplace equation with respect to the variable $x_2$. Taking into account the ill-posedness of boundary value problems for hyperbolic differential equations, the principal part of the boundary conditions is chosen in a special form dictated by the obtained necessary conditions.