Boundary value problems for nonregular systems of differential equations on a half-plane in the class of generalized functions and functions of polynomial growth

The Cauchy problem and the general boundary value problem are considered for nonregular systems of differential equations with constant coefficients in a half-plane. Necessary and sufficient conditions on the initial data are obtained to ensure the solvability of the Cauchy problem in the classes mentioned in the title.
In the study of the general boundary value problem it is assumed that the Lopatinskii conditions hold everywhere except at a finite number of points. It is proved that in the class of functions of arbitrary polynomial growth the inhomogeneous problem is always solvable, while the homogeneous problem has a finite number of linearly independent solutions. A formula for the index is obtained.
Additional conditions on the solutions are indicated, ensuring the unique solvability of the problems. At the end of the paper, the results are illustrated by the example of elliptic second order equations.
Bibliography: 13 titles.