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One Boundary-Value Problem for Elliptic Differential-Operator Equations of the Second Order with Quadratic Spectral Parameter

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Ukrainian Mathematical Journal Aims and scope

The problem of solvability of boundary-value problems for differential-operator equations of the second order on a finite interval is studied in a complex separable Hilbert space H in the case where the same spectral parameter appears in the equation quadratically and, in the boundary conditions, in the form of a linear function and, moreover, the boundary conditions are not separated. The asymptotic behavior of the eigenvalues of one homogeneous abstract boundary-value problem is also investigated. The asymptotic formulas for the eigenvalues are obtained and the possibility of application of the obtained results to partial differential equations is analyzed.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

    B. A. Aliev & N. K. Kurbanova

  2. School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel

    Ya. Yakubov

Authors
  1. B. A. Aliev
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  2. N. K. Kurbanova
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  3. Ya. Yakubov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 6, pp. 734–750, June, 2017.

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Aliev, B.A., Kurbanova, N.K. & Yakubov, Y. One Boundary-Value Problem for Elliptic Differential-Operator Equations of the Second Order with Quadratic Spectral Parameter. Ukr Math J 69, 857–875 (2017). https://doi.org/10.1007/s11253-017-1401-z

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  • DOI: https://doi.org/10.1007/s11253-017-1401-z

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