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Sbornik: Mathematics, 2011, Volume 202, Issue 6, Pages 909–934
DOI: https://doi.org/10.1070/SM2011v202n06ABEH004171 (Mi sm7682) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Approximative compactness and nonuniqueness in variational problems, and applications to differential equations

I. G. Tsar'kov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (388 kB) Citations (5) Russian version article
References:
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DOI: https://doi.org/10.1070/SM2011v202n06ABEH004171
Abstract: The paper is concerned with the study of sets which are approximatively compact with respect to a family of functionals obtained by subtracting affine functionals from some fixed base functional. Nonconvexity of the base functional is shown to imply the minimum in a variational problem with some modified functional is not unique. The results obtained are applied to a specific equation involving the q-Laplacian.
Bibliography: 7 titles.
Keywords: approximative compactness, variational problem, nonlinear differential equation.
Received: 20.01.2010 and 29.09.2010
Bibliographic databases:
Document Type: Article
UDC: 517.518.8+517.972+517.982.256
MSC: 41A65, 35A02
Language: English
Original paper language: Russian
Citation: I. G. Tsar'kov, “Approximative compactness and nonuniqueness in variational problems, and applications to differential equations”, Sb. Math., 202:6 (2011), 909–934
Citation in format AMSBIB
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\by I.~G.~Tsar'kov
\paper Approximative compactness and nonuniqueness in variational problems, and applications to differential equations
\jour Sb. Math.
\yr 2011
\vol 202
\issue 6
\pages 909--934
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Linking options:
  • https://www.mathnet.ru/eng/sm7682
  • https://doi.org/10.1070/SM2011v202n06ABEH004171
  • https://www.mathnet.ru/eng/sm/v202/i6/p133
    • This publication is cited in the following 5 articles:
    1. I. G. Tsar'kov, “$\theta$-metric function in the problem of minimization of functionals”, Izv. Math., 88:2 (2024), 369–388  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. I. G. Tsar'kov, “Chebyshev Sets with Piecewise Continuous Metric Projection”, Math. Notes, 113:6 (2023), 840–849  mathnet  crossref  crossref
    3. A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730  mathnet  crossref  mathscinet
    5. Saint Raymond J., “Characterizing Convex Functions by Variational Properties”, J. Nonlinear Convex Anal., 14:2 (2013), 253–262  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:683
    Russian version PDF:240
    English version PDF:23
    References:100
    First page:21
     
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