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Russian Academy of Sciences. Sbornik. Mathematics, 1993, Volume 75, Issue 1, Pages 247–255
DOI: https://doi.org/10.1070/SM1993v075n01ABEH003382 (Mi sm1474) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the existence of a countable set of solutions in a problem of polaron theory

P. E. Zhidkov
English version PDF (436 kB) Citations (2) Russian version article
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DOI: https://doi.org/10.1070/SM1993v075n01ABEH003382
Abstract: An investigation is made of a certain nonlinear second-order integro-differential equation having numerous applications in various areas of physics (polaron theory, the theory of many-particle quantum systems, and so on). Under certain assumptions it is proved that there is a positive solution, and, moreover, an infinite set of distinct solutions. Use is made of the Lyusternik–Shnirel'man theory of critical points and the fibering method of S. I. Pokhozhaev.
Received: 09.04.1990
Bibliographic databases:
MSC: 34A12, 45J05, 58E05
Language: English
Original paper language: Russian
Citation: P. E. Zhidkov, “On the existence of a countable set of solutions in a problem of polaron theory”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 247–255
Citation in format AMSBIB
\Bibitem{Zhi92}
\by P.~E.~Zhidkov
\paper On the existence of a~countable set of solutions in a problem of polaron theory
\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 75
\issue 1
\pages 247--255
\mathnet{http://mi.mathnet.ru/eng/sm1474}
\crossref{https://doi.org/10.1070/SM1993v075n01ABEH003382}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=1166954}
\zmath{https://zbmath.org/?q=an:0774.45005|0754.45012}
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  • https://doi.org/10.1070/SM1993v075n01ABEH003382
  • https://www.mathnet.ru/eng/sm/v183/i2/p102
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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