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Oscillation Properties of a Multipoint Fourth-Order Boundary-Value Problem with Spectral Parameter in the Boundary Condition

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Abstract

A multipoint fourth-order boundary-value problem with spectral parameter in the boundary condition is considered. It is proved that its spectrum is simple and the system of derivative eigenfunctions has oscillation properties.

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References

  1. N. B. Kerimov and Z. S. Aliev, “Basis properties of a spectral problem with spectral parameter in the boundary condition,” Mat. Sb. 197 (10), 65–86 (2006) [Sb. Math. 197 (10), 1467-1487 (2006)].

    Article  MathSciNet  Google Scholar 

  2. R. Ch. Kulaev, “On the disconjugacy of a differential equation on a graph,” Vladikavkaz. Mat. Zh. 19 (3), 31–40 (2017).

    MathSciNet  Google Scholar 

  3. P. Lancaster, A. Shkalikov, and Q. Ye, “Strongly definitizable linear pencils in Hilbert space,” Integral Equations Operator Theory 17 (3), 338–360 (1993).

    Article  MathSciNet  Google Scholar 

  4. A. A. Vladimirov, “On the problem of oscillation properties of positive differential operators with singular coefficients,” Mat. Zametki 100 (6), 800–806 (2016) [Math. Notes 100 (6), 790–795 (2016)].

    Article  MathSciNet  Google Scholar 

  5. J. Ben Amara and A. A. Vladimirov, “On oscillation of eigenfunctions of a fourth-order problem with spectral parameters in the boundary conditions,” Fundam. Prikl. Mat. 12 (4), 41–52 (2006) [J. Math. Sci. (New York) 150 (5), 2317–2325 (2008)].

    Google Scholar 

  6. J. Ben Amara, A. A. Vladimirov, and A. A. Shkalikov, “Spectral and oscillatory properties of a linear pencil of fourth-order differential operators,” Mat. Zametki 94 (1), 55–67 (2013) [Math. Notes 94 (1), 49–59 (2013)].

    Article  MathSciNet  Google Scholar 

  7. W. Leighton and Z. Nehari, “On the oscillation of solutions of self-adjoint linear differential equations of the fourth order,” Trans. Amer. Math. Soc. 89, 325–377 (1958).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Federal Research Center Computer Science and Control, Russian Academy of Sciences, Moscow, 119333, Russia

    A. A. Vladimirov

  2. Plekhanov Russian State University of Economics, Moscow, 117997, Russia

    E. S. Karulina

Authors
  1. A. A. Vladimirov
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  2. E. S. Karulina
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Corresponding authors

Correspondence to A. A. Vladimirov or E. S. Karulina.

Additional information

Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 6, pp. 854–859.

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Vladimirov, A.A., Karulina, E.S. Oscillation Properties of a Multipoint Fourth-Order Boundary-Value Problem with Spectral Parameter in the Boundary Condition. Math Notes 106, 899–903 (2019). https://doi.org/10.1134/S0001434619110257

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  • DOI: https://doi.org/10.1134/S0001434619110257

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