The Discrete Spectrum Of Some Classes Of Self-Adjoint Differential Operators

In this paper, we study the discrete spectrum of some classes of self-adjoint differen-tial operators generated by the symmetry differential expression. First of all, we obtain the necessary and sufficient conditions for the spectrum of three-term and fourth ordci self-adjoint differential operator to be discrete. Further more, we obtain the discreteness of the spectrum for high order self-adjoint differential operators.The last,we study the discreteness of spectra of three-term and fourth order self-adjoint vector differential op-erators,and obtain the sufficient conditions for the discrete spectrum.