Abstract
Solvability of mixed boundary-value problems in domains with cylindrical outlets to infinity is investigated for a certain class of non-self-adjoint differential operator-matrices., The structure of these matrices is such that the corresponding asymmetric quadratic forms possess a polynomial property, i.e., they degenerate only on finite-dimensional lineals of vector polynomials. With the help of elementary algebraic operations, this property enables one to indicate some attributes of boundary-value problems, namely, to calculate the operator index, to describe the kernel and co-kernel of an operator, to find an asymptotic behavior of solutions at infinity, etc. Bibliography: 16 titles.
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