Correctness conditions for high-order differential equations with unbounded coefficients

Abstract

We give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent. MSC: Primary 34B40; secondary 47E05