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Mathematics of the USSR-Sbornik, 1992, Volume 71, Issue 2, Pages 427–446
DOI: https://doi.org/10.1070/SM1992v071n02ABEH001404
(Mi sm1249)
 

This article is cited in 31 scientific papers (total in 31 papers)

Spectra of nonlinear differential equations and widths of Sobolev classes

A. P. Buslaev, V. M. Tikhomirov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: The authors study the problem of Kolmogorov widths of Sobolev classes Wrp([0,1])Wrp([0,1]) of functions in the LqLq-metric, pq, and the connected questions of the existence and uniqueness of the spectra of nonlinear equations.
Received: 27.04.1990
Bibliographic databases:
UDC: 517.5+517.9
MSC: 41A46, 34B15, 46E35
Language: English
Original paper language: Russian
Citation: A. P. Buslaev, V. M. Tikhomirov, “Spectra of nonlinear differential equations and widths of Sobolev classes”, Math. USSR-Sb., 71:2 (1992), 427–446
Citation in format AMSBIB
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\by A.~P.~Buslaev, V.~M.~Tikhomirov
\paper Spectra of nonlinear differential equations and widths of Sobolev classes
\jour Math. USSR-Sb.
\yr 1992
\vol 71
\issue 2
\pages 427--446
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Linking options:
  • https://www.mathnet.ru/eng/sm1249
  • https://doi.org/10.1070/SM1992v071n02ABEH001404
  • https://www.mathnet.ru/eng/sm/v181/i12/p1587
  • This publication is cited in the following 31 articles:
    1. Lyonell Boulton, Jan Lang, “The eigenvalues and eigenfunctions of the non-linear equation associated to second order Sobolev embeddings”, Nonlinear Analysis, 236 (2023), 113362  crossref
    2. Vasil'eva A.A., “Widths of Weighted Sobolev Classes With Constraints F(a) = Center Dot Center Dot Center Dot = F(K-1)(a) = F(K)(B) = Center Dot Center Dot Center Dot = F(R-1)(B)=0 and the Spectra of Nonlinear Differential Equations”, Russ. J. Math. Phys., 24:3 (2017), 376–398  crossref  mathscinet  zmath  isi  scopus
    3. X.L.i Wang, G.R.idi Wu, “On n-widths of a Sobolev function class in Orlicz spaces”, Acta. Math. Sin.-English Ser, 31:9 (2015), 1475  crossref  mathscinet  zmath
    4. A.A. Vasil’eva, “Kolmogorov and linear widths of the weighted Besov classes with singularity at the origin”, Journal of Approximation Theory, 167 (2013), 1  crossref  mathscinet
    5. A. A. Vasil'eva, “Widths of weighted Sobolev classes on a John domain”, Proc. Steklov Inst. Math., 280 (2013), 91–119  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. A. A. Vasilyeva, “Kolmogorov widths and approximation numbers of Sobolev classes with singular weights”, St. Petersburg Math. J., 24:1 (2013), 1–27  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    7. Guo Feng, “Bernstein Widths of Some Classes of Functions Defined by a Self-Adjoint Operator”, Journal of Applied Mathematics, 2012 (2012), 1  crossref  mathscinet
    8. Vasil'eva A.A., “Kolmogorov Widths of Weighted Sobolev Classes on a Domain for a Special Class of Weights. II”, Russian Journal of Mathematical Physics, 18:4 (2011), 465–504  crossref  mathscinet  zmath  isi
    9. Vasil'eva A.A., “Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights”, Russian Journal of Mathematical Physics, 18:3 (2011), 353–385  crossref  mathscinet  zmath  isi
    10. A. A. Vasil'eva, “Estimates for the widths of weighted Sobolev classes”, Sb. Math., 201:7 (2010), 947–984  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Guo Feng, Gen Sun Fang, “Bernstein n-widths for classes of convolution functions with kernels satisfying certain oscillation properties”, Acta Math Sinica, 25:3 (2009), 393  crossref  mathscinet  zmath  isi
    12. Feng Guo, “Exact Values of Bernstein n-Widths for Some Classes of Periodic Functions with Formal Self-Adjoint Linear Differential Operators”, J Inequal Appl, 2008 (2008), 1  crossref  mathscinet  isi
    13. Yuri V. Egorov, Differential Operators and Related Topics, 2000, 101  crossref
    14. Jiang Y., Liu Y., “Average B-Width and Infinite-Dimensional G-Width of Some Smooth Function Classes on the Line”, Chin. Sci. Bull., 43:10 (1998), 810–812  crossref  mathscinet  zmath  isi
    15. R. Kh. Sadikova, “Inequalities for sourcewise representable functions and their applications”, Math. Notes, 62:4 (1997), 469–479  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. Yuri V. Egorov, “On a Kondratiev problem1”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 324:5 (1997), 503  crossref  mathscinet  zmath
    17. Babenko V., Kofanov V., Pichugov S., “On Exact Inequalities of Landau-Hadamard-Kolmogorov Type for Multivariate Functions”, Dokl. Akad. Nauk, 356:1 (1997), 7–9  mathnet  mathscinet  zmath  isi
    18. Tikhomirov V., “On Extremal Subspaces of Functional Classes Defined by Cyclic Variation Diminishing Kernels”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1997, no. 4, 16–19  mathscinet  zmath  isi
    19. A. P. Buslaev, G. G. Magaril-Il'yaev, Nguyen Thien Nam, “Exact values of Bernstein widths of Sobolev classes of periodic functions”, Math. Notes, 58:1 (1995), 770–774  mathnet  crossref  mathscinet  zmath  isi
    20. V. M. Tikhomirov, “Harmonics and splines as optimal tools for approximation and recovery”, Russian Math. Surveys, 50:2 (1995), 355–402  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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