Buryachenko E. "Solvability of boundary value problems for high-order differential equations of principal type in a disk."

In the thesis the properties of solutions of boundary value problems for the high-order differential equations with the constant complex coefficients are investigated. It has been obtained a criterion of solutions uniqueness breakdown of the even order 2m differential equations of a principal type. It is fond necessary and sufficient conditions for the solutions uniqueness breakdown of the Dirichlet problem for the fourth order differential equations whose characteristics are parallel and (or) have no angles of slope. The complex characteristics billiard for the fourth order differential equations is considered in the work in first.