IJPAM: Volume 89, No. 3 (2013)
THE SCHRODINGER OPERATOR WITH
A NON-LOCAL PERTURBATION




Akhmet Yasawi International Kazakh-Turkish University
29, Sattarkhanov Str., 161200, Turkistan, KAZAKHSTAN

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 .
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