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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 4, Pages 25–33 (Mi ufa299)  

This article is cited in 1 scientific paper (total in 1 paper)

On perturbation of a Schrödinger operator on axis by narrow potentials

A. R. Bikmetov, V. F. Vil'danova, I. Kh. Khusnullin

Bashkir State Pedagogical University, Ufa, Russia

Abstract: We consider a Schrödinger operator on the axis with two complex-valued potentials depending on two small parameters. One these parameters describes the length of the supports of the potentials, while the other corresponds to the maximal values of the absolute values of the potentials. We obtain the sufficient condition ensuring the emergence of an eigenvalues from the threshold of the essential spectrum. The asymptotics for this eigenvalue is constructed.

Keywords: Schrödinger operator, perturbation, asymptotics.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-97024 р_поволжье_а
Ministry of Education and Science of the Russian Federation


Full text: PDF file (456 kB)
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English version:
Ufa Mathematical Journal, 2015, 7:4, 24–31 (PDF, 324 kB); https://doi.org/10.13108/2015-7-4-24

Bibliographic databases:

UDC: 517.928.1
MSC: 35J10, 34E10
Received: 18.08.2015

Citation: A. R. Bikmetov, V. F. Vil'danova, I. Kh. Khusnullin, “On perturbation of a Schrödinger operator on axis by narrow potentials”, Ufimsk. Mat. Zh., 7:4 (2015), 25–33; Ufa Math. J., 7:4 (2015), 24–31

Citation in format AMSBIB
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\by A.~R.~Bikmetov, V.~F.~Vil'danova, I.~Kh.~Khusnullin
\paper On perturbation of a~Schr\"odinger operator on axis by narrow potentials
\jour Ufimsk. Mat. Zh.
\yr 2015
\vol 7
\issue 4
\pages 25--33
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\transl
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 4
\pages 24--31
\crossref{https://doi.org/10.13108/2015-7-4-24}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. Kh. Khusnullin, “Vozmuschenie volnovoda uzkim potentsialom”, Tr. IMM UrO RAN, 23, no. 2, 2017, 274–284  mathnet  crossref  elib
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