FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 41-52

**On oscillation of eigenfunctions of a fourth-order problem with
spectral parameter in boundary condition**

J. Ben Amara

A. A. Vladimirov

Abstract

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In the paper, we study the problem on the number of zeros of
eigenfunctions of the fourth-order boundary-value problem with
spectral and physical parameters in the boundary conditions.
We show that the number of zeros of the eigenfunctions corresponding
to eigenvalues of positive type behaves in a usual way (it is
equal to the serial number of an eigenvalue increased
by $1$),
but, however, the number of zeros of the eigenfunction corresponding
to an eigenvalue of negative type can be arbitrary.
In the case of a sufficient smoothness of coefficients of the
differential expression, we write the asymptotics in the physical
parameter for such a number.

Location: http://mech.math.msu.su/~fpm/eng/k06/k064/k06403h.htm

Last modified: February 17, 2007