ASYMPTOTIC DISTRIBUTION OF EIGENVALUES FOR FOURTH-ORDER BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS COEFFICIENTS AN

Abstract

We investigate a fourth-order boundary value problem with discontinuous coe¢ cients, functional many points and transmission conditions.In this problem, boundary conditions contain not only endpoints of the considered interval, but also a point of discontinuity, a ...nite number internalpoints and abstract linear functionals. We discuss asymptotic distribution ofits eigenvalues. Finally, we obtain asymptotic formulas for the eigenvalues ofthe problem in sectors of the complex plane.

We investigate a fourth-order boundary value problem with discontinuous coe¢ cients, functional many points and transmission conditions.In this problem, boundary conditions contain not only endpoints of the considered interval, but also a point of discontinuity, a ...nite number internalpoints and abstract linear functionals. We discuss asymptotic distribution ofits eigenvalues. Finally, we obtain asymptotic formulas for the eigenvalues ofthe problem in sectors of the complex plane.