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Mat. Sb., 1990, Volume 181, Number 12, Pages 1587–1606 (Mi msb1249)  

This article is cited in 29 scientific papers (total in 29 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

Abstract: The authors study the problem of Kolmogorov widths of Sobolev classes $W_p^r([0,1])$ of functions in the $L_q$-metric, $p\geqslant q$, and the connected questions of the existence and uniqueness of the spectra of nonlinear equations.

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English version:
Mathematics of the USSR-Sbornik, 1992, 71:2, 427–446

Bibliographic databases:

UDC: 517.5+517.9
MSC: 41A46, 34B15, 46E35
Received: 27.04.1990

Citation: A. P. Buslaev, V. M. Tikhomirov, “Spectra of nonlinear differential equations and widths of Sobolev classes”, Mat. Sb., 181:12 (1990), 1587–1606; Math. USSR-Sb., 71:2 (1992), 427–446

Citation in format AMSBIB
\by A.~P.~Buslaev, V.~M.~Tikhomirov
\paper Spectra of nonlinear differential equations and widths of Sobolev classes
\jour Mat. Sb.
\yr 1990
\vol 181
\issue 12
\pages 1587--1606
\jour Math. USSR-Sb.
\yr 1992
\vol 71
\issue 2
\pages 427--446

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    This publication is cited in the following articles:
    1. G. G. Magaril-Il'yaev, “Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line”, Math. USSR-Sb., 74:2 (1993), 381–403  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Magarililyayev G., “Average Dimensionality and Widths of Functional Classes on Straight-Line”, 318, no. 1, 1991, 35–38  isi
    3. Buslayev A., “On Bernstein-Nikolsky Inequalities and Widths of Sobolev Spaces of Functions”, Dokl. Akad. Nauk, 323:2 (1992), 202–205  mathnet  mathscinet  isi
    4. A. P. Buslaev, “Some properties of the spectrum of nonlinear equations of Sturm–Liouville type”, Russian Acad. Sci. Sb. Math., 80:1 (1995), 1–14  mathnet  crossref  mathscinet  zmath  isi
    5. Nguyen Thien Nam, “Spectrum of nonlinear integral equations and the widths of function classes”, Math. Notes, 53:4 (1993), 424–429  mathnet  crossref  mathscinet  zmath  isi  elib
    6. A. P. Buslaev, M. V. Yashina, “Numerical methods in problems of best approximation by splines and nonlinear spectrum analysis”, Comput. Math. Math. Phys., 33:10 (1993), 1287–1297  mathnet  mathscinet  zmath  isi
    7. Fang G., Liu Y., “Average Width and Optimal Interpolation of the Sobolev-Wiener Class W(Pq)R(R) in the Metric l(Q)(R)”, J. Approx. Theory, 74:3 (1993), 335–352  crossref  mathscinet  zmath  isi
    8. Chen D., Zhang J., “On the 2N-Widths of a Periodic Sobolev Class”, J. Approx. Theory, 75:1 (1993), 8–24  crossref  mathscinet  zmath  isi
    9. Fisher S., Stessin M., “On N-Widths of Classes of Holomorphic-Functions with Reproducing Kernels”, Ill. J. Math., 38:4 (1994), 589–615  crossref  mathscinet  zmath  isi
    10. Bratus A., “The Properties of Solutions of a Class of Isoperimetric Problems of Stability Optimization”, Pmm-J. Appl. Math. Mech., 58:6 (1994), 1029–1038  crossref  mathscinet  zmath  isi
    11. 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
    12. 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
    13. MagarilIlyaev G., Tikhomirov V., “The Exact Value of the Widths of Functional Classes in l(2)”, Dokl. Akad. Nauk, 344:5 (1995), 583–585  mathnet  mathscinet  isi
    14. R. Kh. Sadikova, “Inequalities for sourcewise representable functions and their applications”, Math. Notes, 62:4 (1997), 469–479  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. Yuri V. Egorov, “On a Kondratiev problem1”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 324:5 (1997), 503  crossref  mathscinet  zmath
    16. 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
    17. 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
    18. 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
    19. 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
    20. 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
    21. 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
    22. 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
    23. 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
    24. 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
    25. Guo Feng, “Bernstein Widths of Some Classes of Functions Defined by a Self-Adjoint Operator”, Journal of Applied Mathematics, 2012 (2012), 1  crossref  mathscinet
    26. 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
    27. 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
    28. 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
    29. 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
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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