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Mat. Sb., 2000, Volume 191, Number 3, Pages 43–52 (Mi msb461)  

This article is cited in 17 scientific papers (total in 17 papers)

Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm–Liouville type

P. E. Zhidkov

Joint Institute for Nuclear Research

Abstract: For a non-linear eigenvalue problem similar to a linear Sturm–Liouville problem the properties of the spectrum and the eigenfunctions are analysed. The system of eigenfunctions is shown to be a Riesz basis in $L_2$.

DOI: https://doi.org/10.4213/sm461

Full text: PDF file (235 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2000, 191:3, 359–368

Bibliographic databases:

UDC: 517.927.25
MSC: 34B25, 34B15, 47A75
Received: 03.11.1998 and 14.07.1999

Citation: P. E. Zhidkov, “Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm–Liouville type”, Mat. Sb., 191:3 (2000), 43–52; Sb. Math., 191:3 (2000), 359–368

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Zhidkov P.E., “Basis Properties of Eigenfunctions of Nonlinear Sturm-Liouville Problems”, Electron. J. Differ. Equ., 2000, 28  mathscinet  zmath  isi
    2. Zhidkov P., Korteweg-de Vries and nonlinear Schröginger equations: qualitative theory, Lecture Notes in Math., 1756, Springer-Verlag, Berlin, 2001, vi+147 pp.  crossref  mathscinet  zmath  isi
    3. Courteille, PW, “Bose–Einstein condensation of trapped atomic gases”, Laser Physics, 11:6 (2001), 659  isi  elib
    4. Zhidkov, PE, “On the Bari basis property of the eigenfunction system of a nonlinear integro-differential equation”, Differential Equations, 38:9 (2002), 1260  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Makin A.S., “On the basis property of a system of eigenfunctions of a nonlinear spectral problem”, Differ. Equ., 39:5 (2003), 644–651  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. Zhidkov P.E., “An analog of the Fourier transform associated with a nonlinear one-dimensional Schrödinger equation”, Nonlinear Anal., 52:3 (2003), 737–754  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. Delattre C., Dochain D., Winkin J., “Sturm-Liouville Systems Are Riesz-Spectral Systems”, Int. J. Appl. Math. Comput. Sci., 13:4 (2003), 481–484  mathscinet  zmath  isi
    8. Peter Zhidkov, “On an inverse eigenvalue problem for a semilinear Sturm–Liouville operator”, Nonlinear Analysis: Theory, Methods & Applications, 68:3 (2008), 639  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Zhidkov P., “On On the existence, uniqueness, and basis properties of radial eigenfunctions of a semilinear second-order elliptic equation in a ball”, Int. J. Math. Math. Sci., 2009, 243048, 11 pp.  crossref  mathscinet  zmath
    10. Zhidkov P., “On the eigenfunction expansions associated with semilinear Sturm-Liouville-type problems”, Nonlinear Anal., 70:12 (2009), 4123–4139  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    11. Djakov P., Mityagin B., “Bari-Markus property for Riesz projections of Hill operators with singular potentials”, Functional Analysis and Complex Analysis, Contemporary Mathematics Series, 481, 2009, 59–80  crossref  mathscinet  zmath  isi
    12. D. V. Valovik, Yu. G. Smirnov, “On the problem of propagation of nonlinear coupled TE–TM waves in a layer”, Comput. Math. Math. Phys., 54:3 (2014), 522–536  mathnet  crossref  crossref  isi  elib  elib
    13. D.V. Valovik, “Integral dispersion equation method to solve a nonlinear boundary eigenvalue problem”, Nonlinear Analysis: Real World Applications, 20 (2014), 52  crossref  mathscinet  zmath  scopus  scopus  scopus
    14. Valovik D.V., Kurseeva V.Yu., “On the eigenvalues of a nonlinear spectral problem”, Differ. Equ., 52:2 (2016), 149–156  crossref  mathscinet  zmath  isi  scopus
    15. D. V. Valovik, “The spectral properties of some nonlinear operators of Sturm-Liouville type”, Sb. Math., 208:9 (2017), 1282–1297  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    16. Olgar H., Mukhtarov O.Sh., “Weak Eigenfunctions of Two-Interval Sturm-Liouville Problems Together With Interaction Conditions”, J. Math. Phys., 58:4 (2017), 042201  crossref  mathscinet  zmath  isi  elib  scopus
    17. Olgar H., Mukhtarov O.Sh., Aydemir K., “Some Properties of Eigenvalues and Generalized Eigenvectors of One Boundary Value Problem”, Filomat, 32:3 (2018), 911–920  crossref  mathscinet  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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