ON SOME SPECTRAL PROBLEMS FOR HIGHER ORDER DIFFERENTIAL OPERATOR EQUATION, I

Abstract

The aim of the paper is first to study domains of definitions in terms of boundary conditions  of minimal and maximal operators, as well as selfadjoint extensions of the minimal operator associated with a fourth-order differential operator equation. Further, we give necessary and sufficient conditions for those operators to have a purely discrete or continuous spectrum, to exist extension with resolvent from σp, study asymptotics of spectrum in case of pure discrete spectrum