Asymptotic formulas with arbitrary order for nonselfadjoint differential operators

Abstract

We obtain asymptotic formulas with arbitrary order of accuracy for the eigenvalues and eigenfunctions of a nonselfadjoint ordinary differential operator of order n whose coefficients are Lebesgue integrable on [0, 1] and the boundary conditions are strongly regular. The orders of asymptotic formulas are independent of smoothness of the coefficients.

Bounds for the spectrum of a matrix differential operator with a damping term

“…The eigenvalues and completeness for scalar regular and simply irregular two-point higher-order differential operator are deeply investigated in the monographs [11,12]. The paper [3] is concerned with the boundary value problem y (n) (x) + p 2 (x)y (n−2) (x) + · · · + p n−1 (x)y (x) + p n (x)y(x) = λy(x), 0 ≤ x ≤ 1 under certain boundary conditions. Besides, the coefficients are nonsmooth in general.…”