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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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\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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  • https://doi.org/10.1070/SM2011v202n06ABEH004171
  • https://www.mathnet.ru/eng/sm/v202/i6/p133
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:639
    Russian version PDF:227
    English version PDF:15
    References:86
    First page:21
     
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