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Asymptotic Behavior of Eigenvalues of a Boundary Value Problem for a Second-Order Elliptic Differential-Operator Equation with Spectral Parameter Quadratically Occurring in the Boundary Condition

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Abstract

The asymptotic behavior of eigenvalues of a boundary value problem for a secondorder differential-operator equation in a separable Hilbert space on a finite interval is studied for the case in which the same spectral parameter occurs linearly in the equation and quadratically in one of the boundary conditions. We prove that the problem has a sequence of eigenvalues converging to zero.

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References

  1. Yakubov, S.Ya., A boundary value problem for the Laplace equation with nonclassical spectral asymptotics, Sov. Math. Dokl., 1982, vol. 26, pp. 276–279.

    MATH  Google Scholar 

  2. Gorbachuk, V.I. and Rybak, M.A., On the boundary value problems for the operator Sturm–Liouville equation with a spectral parameter in the equation and in the boundary condition, in Direct and Inverse Problems of Scattering Theory, Collect. Sci. Papers, Kiev, 1981, pp. 3–16.

    Google Scholar 

  3. Rybak, M.A., Asymptotic distribution of the eigenvalues of some boundary value problems for Sturm–Liouville operator equations, Ukr. Math. J., 1980, vol. 32, pp. 159–162.

    Article  MATH  Google Scholar 

  4. Aliev, B.A., Asymptotic behavior of the eigenvalues of a boundary value problem for a second-order elliptic operator-differential equation, Ukr. Math. J., 2006, vol. 58, no. 8, pp. 1298–1306.

    Article  MathSciNet  Google Scholar 

  5. Aliev, B.A. and Kurbanova, N.K., Asymptotic behavior of eigenvalues of a boundary value problem for a second order elliptic differential-operator equation, in Proc. Inst. Math. Mech.: Natl. Acad. Sci. Azerb., 2014, vol. 40, Spec. Iss., pp. 23–29.

    Google Scholar 

  6. Aliev, B.A., Kurbanova, N.K., and Yakubov, Ya., Solvability of the abstract Regge boundary value problem and asymptotic behavior of eigenvalues of one abstract spectral problem, Riv. Mat. Univ. Parma, 2015, vol. 6, pp. 241–265.

    MathSciNet  MATH  Google Scholar 

  7. Kapustin, N.Yu., On a spectral problem in the theory of the heat operator, Differ. Equations, 2009, vol. 45, no. 10, pp. 1509–1511.

    Article  MathSciNet  Google Scholar 

  8. Kapustin, N.Yu., On the uniform convergence in C1 of Fourier series for a spectral problem with squared spectral parameter in a boundary condition, Differ. Equations, 2011, vol. 47, no. 10, pp. 1408–1413.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, AZ1141, Azerbaijan

    B. A. Aliev

  2. Baku State Pedagogical University, Baku, AZ1000, Azerbaijan

    B. A. Aliev

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  1. B. A. Aliev
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Correspondence to B. A. Aliev.

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Original Russian Text © B.A. Aliev, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 9, pp. 1282–1286.

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Aliev, B.A. Asymptotic Behavior of Eigenvalues of a Boundary Value Problem for a Second-Order Elliptic Differential-Operator Equation with Spectral Parameter Quadratically Occurring in the Boundary Condition. Diff Equat 54, 1256–1260 (2018). https://doi.org/10.1134/S0012266118090124

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  • DOI: https://doi.org/10.1134/S0012266118090124

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