On the spectral properties of a class of high-order differential operators with operator coefficients

Abstract

In this paper, we study one class of high-order differential operators. The main feature of these operators is their nonsemi-boundedness. The dependence of operator coefficients on variables creates additional difficulties in the study. In the course of the study, the conditions for the existence of a solution and separability were first found. Also studied are the questions of the smoothness of solutions and on the spectrum of boundary value problems for unbounded differential equations with variable operator coefficients