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Degenerate Three-Point Boundary Conditions

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Abstract

For the differential equation \(y^{\prime \prime \prime }(x)=\lambda y(x) \) on the interval \([0,1] \), we consider the three-point eigenvalue problem \(a_i y^{(i-1)}(0)+y(c)+b_i y^{(i-1)}(1)=0\), \(i=1,2,3 \), where \(\lambda \) is the spectral parameter, the point \(c\in (0,1) \) is fixed, and \(a_i \) and \(b_i \), \(i=1,2,3\), are some complex numbers. Necessary and sufficient conditions that the coefficients \(a_i \) and \(b_i \) must satisfy for the indicated three-point problem to have degenerate boundary conditions are obtained.

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Funding

This research was facilitated by the Moscow Center for Fundamental and Applied Mathematics. The research by A.M. Akhtyamov was carried out using public funds allocated for 2019–2022 State Order, project no. 0246-2019-0088, and supported by the Russian Foundation for Basic Research, projects nos. 18-51-06002-Az_a and 18-01-00250_a; the research by Ya.T. Sultanaev was supported by the Russian Foundation for Basic Research, projects nos. 18-51-06002-Az_a and 18-01-00250_a.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. A. Sadovnichii

  2. Mavlyutov Institute of Mechanics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, 450054, Russia

    Ya. T. Sultanaev

  3. Akmulla Bashkir State Pedagogical University, Ufa, 450008, Russia

    Ya. T. Sultanaev

  4. Bashkir State University, Ufa, 450076, Russia

    A. M. Akhtyamov

Authors
  1. V. A. Sadovnichii
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  2. Ya. T. Sultanaev
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  3. A. M. Akhtyamov
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Corresponding authors

Correspondence to V. A. Sadovnichii, Ya. T. Sultanaev or A. M. Akhtyamov.

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Translated by V. Potapchouck

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Sadovnichii, V.A., Sultanaev, Y.T. & Akhtyamov, A.M. Degenerate Three-Point Boundary Conditions. Diff Equat 56, 1545–1549 (2020). https://doi.org/10.1134/S00122661200120034

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  • DOI: https://doi.org/10.1134/S00122661200120034

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