On conditions of regular solvability for two classes of third-order operator-differential equations in a fourth-order Sobolev-type space.

In this paper, we study two classes of operator-differential equations of the third order with a multiple characteristic, considered on the whole axis. We introduce the concept of a smooth regular solution of order 1 and obtain sufficient conditions for the "smoothly" regular solvability of these equations. [ABSTRACT FROM AUTHOR]