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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, Issue 3, Pages 104–113 (Mi vuu30)  

This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

Quasi-levels of the discrete Schrödinger equation with a decreasing potential on a graph

T. S. Tinyukovaa, Yu. P. Chuburinb

a Udmurt State University
b Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences, Izhevsk

Abstract: We consider the discrete Schrödinger operator perturbed by a decreasing potential of the form $\varepsilon V$ defined on a graph the nodes of which lie on the union of two intersected straight lines. We prove that non-vanishing quasi-levels do not exist in the neighbourhood of zero for a small $\varepsilon$.

Keywords: discrete Schrödinger equation, eigenvalue, resonance.

Full text: PDF file (326 kB)
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Document Type: Article
UDC: 517.958:530.145.6
MSC: 81Q10, 81Q15
Received: 10.05.2009

Citation: T. S. Tinyukova, Yu. P. Chuburin, “Quasi-levels of the discrete Schrödinger equation with a decreasing potential on a graph”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, no. 3, 104–113

Citation in format AMSBIB
\Bibitem{TinChu09}
\by T.~S.~Tinyukova, Yu.~P.~Chuburin
\paper Quasi-levels of the discrete Schr\"odinger equation with a~decreasing potential on a~graph
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2009
\issue 3
\pages 104--113
\mathnet{http://mi.mathnet.ru/vuu30}


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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. T. S. Tinyukova, “Uravnenie Lippmana–Shvingera dlya kvantovykh provolok”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 1, 99–104  mathnet
    2. T. S. Tinyukova, “Rasseyanie v sluchae diskretnogo operatora Shredingera dlya peresekayuschikhsya kvantovykh provolok”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 3, 74–84  mathnet
    3. T. S. Tinyukova, Yu. P. Chuburin, “Diskretnoe uravnenie Shredingera dlya kvantovogo volnovoda”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 80–93  mathnet
    4. L. E. Morozova, “Zadacha rasseyaniya dlya diskretnogo operatora Shredingera s “rezonansnym” potentsialom na grafe”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 1, 29–34  mathnet
    5. T. S. Tinyukova, “Issledovanie raznostnogo uravneniya Shredingera dlya nekotorykh fizicheskikh modelei”, Izv. IMI UdGU, 2013, no. 2(42), 3–57  mathnet
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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