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

Authors: ARAZ R. ALIEV, NAZILA L. MURADOVA

Abstract: 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.

Keywords: Operator-differential equation, Sobolev-type space, smooth regular solution, operator pencils, eigenvalue

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