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Matematicheskie Zametki, 2017, Volume 102, Issue 2, Pages 197–215
DOI: https://doi.org/10.4213/mzm11430 (Mi mzm11430) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Trace of Order (−1)(−1) for a String with Singular Weight

A. S. Ivanov, A. M. Savchuk

Lomonosov Moscow State University
Full-text PDF (602 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm11430
Abstract: The Sturm–Liouville problem on a finite closed interval with potential and weight of first order of singularity is studied. Estimates for the ss-numbers and eigenvalues of the corresponding integral operator are obtained. The spectral trace of first negative order is evaluated in terms of the integral kernel. The obtained theoretical results are illustrated by examples.
Keywords: spectral asymptotics, Sturm–Liouville problem, spectral trace.
Funding agency Grant number
Russian Science Foundation 14-01-00754
This work was supported by the Russian Science Foundation under grant 14-01-00754.
Received: 31.10.2016
Revised: 01.02.2017
English version:
Mathematical Notes, 2017, Volume 102, Issue 2, Pages 164–180
DOI: https://doi.org/10.1134/S0001434617070197
Bibliographic databases:
Document Type: Article
UDC: 517.927.2
Language: Russian
Citation: A. S. Ivanov, A. M. Savchuk, “Trace of Order (−1)(−1) for a String with Singular Weight”, Mat. Zametki, 102:2 (2017), 197–215; Math. Notes, 102:2 (2017), 164–180
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm11430
  • https://doi.org/10.4213/mzm11430
  • https://www.mathnet.ru/eng/mzm/v102/i2/p197
    • This publication is cited in the following 7 articles:
    1. M. B. Zvereva, “The Problem of Deformations of a Singular String with a Nonlinear Boundary Condition”, Lobachevskii J Math, 45:1 (2024), 555  crossref
    2. D. A. Chechin, A. D. Baev, S. A. Shabrov, “Ob odnoi granichnoi zadache s razryvnymi resheniyami i silnoi nelineinostyu”, Materialy Voronezhskoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 4, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 193, VINITI RAN, M., 2021, 153–157  mathnet  crossref  elib
    3. M. Kamenskii, Fitte Paul Raynaud, N.-Ch. Wong, M. Zvereva, “A model of deformations of a discontinuous Stieltjes string with a nonlinear boundary condition”, J. Nonlinear Var. Anal., 5:5 (2021), 737–759  crossref  mathscinet  isi  scopus
    4. A. S. Ivanov, “Refining eigenvalue estimates for a string with a singular weight”, Differ. Equ., 57:10 (2021), 1292–1298  crossref  mathscinet  isi  scopus
    5. Kamenskii M., Wen Ch.-F., Zvereva M., “On a Variational Problem For a Model of a Stieltjes String With a Backlash At the End”, Optimization, 69:9 (2020), 1935–1959  crossref  mathscinet  isi
    6. A. D. Baev, D. A. Chechin, M. B. Zvereva, S. A. Shabrov, “Stieltjes differential in impulse nonlinear problems”, Dokl. Math., 101:1 (2020), 5–8  mathnet  crossref  crossref  zmath  elib
    7. A. S. Ivanov, “Traces of higher negative orders for a string with a singular weight”, Differ. Equ., 54:10 (2018), 1310–1320  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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