IJPAM: Volume 89, No. 3 (2013)

STUDY BASICITY OF ROOT FUNCTIONS OF
THE SCHRODINGER OPERATOR WITH
A NON-LOCAL PERTURBATION

N.S. Imanbayev$^1$, B. Kalimbetov$^2$, A.M. Sarsenbi$^3$
$^{1,2}$Department of Mathematics
Akhmet Yasawi International Kazakh-Turkish University
29, Sattarkhanov Str., 161200, Turkistan, KAZAKHSTAN
$^3$Department of Mathematics
M.O. Auezov South Kazakhstan State University
5, Tauke Khan Str., 160012, Shymkent, KAZAKHSTAN


Abstract. The asymptotics of the eigenvalues is received, and conclusions about the stability and instability of the basis property of the system of eigenfunctions and associated functions of the Schrodinger operator for various occasions of the disarmed regularity of the boundary conditions are done. In the paper there is considered the Samarsky - Ionkin spectral problem for the Schrodinger equation with an integral perturbation in the boundary conditions. It is assumed that the unperturbed problem has a system of eigenfunctions forming a Riesz basis in $ L_2 (0,1) $ . It is shown that the basis property of the systems of root functions of a problem can be varied under any arbitrarily small variation of the kernel of the integral perturbation.

Received: October 10, 2013

AMS Subject Classification: 80M22, 34B10

Key Words and Phrases: basis, Samarsky-Ionkin problem, perturbation, eigenfunctions, eigenvalues

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DOI: 10.12732/ijpam.v89i3.13 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 3