On some spectral problems for higher order differential operator equation, I

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 ?p, study asymptotics of spectrum in case of pure discrete spectrum.