The Completeness Of Eigenvalue Problem Eigenfunction For A4×4Differential Equation With Periodic Boundary Conditions

In this paper, the completeness be studied for eigenfunction system of a periodic boundary value problem by means of the theory of functional analysis First the symmetry of the differential operator be proved and the entire function ω (x) be obtained, whose zero set coincides with the set of the corresponding eigenvalue of the operator. And then the self-adjoint and compact be obtained of the differential operator. Finally the completeness of the eigenfunction system above periodic boundary value problem be proved...