двухточечные краевые условия

On Multiple Completeness of the Root Functions for a Class of the Pencils of Differential Operators

Authors: Rykhlov V. S.

A polinomial pencil of ordinary differential operators of n-th order generated by a homogeneous differential expression with constant coefficients and by two-point boundary conditions of a special structure with lcondition sinzero only (1 ≤ l ≤ n−1) isconsidered in the space L 2 [0,1]. The case is studied, when the roots of the characteristic equation lieonaray coming from theorigin. Asufficient condition of m-fold completeness of the system of root functions for m ≤ n−l inthe space L 2 [0,1] isfound. Anaccuracy of obtained result is shown.

On 2-fold completeness of the eigenfunctions for the strongly irregular quadratic pencil of differential operators of second order

Authors: Parfilova O. V.

 A class of strongly irregular pencils of ordinary differential operators of second order with constant coefficients is considered. The roots of the characteristic equation of the pencils from this class are supposed to lie on a straight line coming through the origin and on the both side of the origin. Exact interval on which the system of eigenfunctions is 2-fold complete in the space of square summable functions is finded.