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Nonlinear spectral problem for a self-adjoint vector differential equation

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Abstract

We consider a spectral problem that is nonlinear in the spectral parameter for a self-adjoint vector differential equation of order 2n. The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the spectral parameter, we present a method for counting the eigenvalues of the problem in a given interval. If the boundary conditions are independent of the spectral parameter, then we define the notion of number of an eigenvalue and give a method for computing this number as well as the set of numbers of all eigenvalues in a given interval. For an equation considered on an unbounded interval, under some additional assumptions, we present a method for approximating the original singular problem by a problem on a finite interval.

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Authors and Affiliations

  1. Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow, 119333, Russia

    A. A. Abramov & L. F. Yukhno

  2. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Moscow, 125047, Russia

    A. A. Abramov & L. F. Yukhno

Authors
  1. A. A. Abramov
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  2. L. F. Yukhno
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Correspondence to A. A. Abramov.

Additional information

Original Russian Text © A.A. Abramov, L.F. Yukhno, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 7, pp. 927–934.

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Abramov, A.A., Yukhno, L.F. Nonlinear spectral problem for a self-adjoint vector differential equation. Diff Equat 53, 900–907 (2017). https://doi.org/10.1134/S0012266117070060

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  • DOI: https://doi.org/10.1134/S0012266117070060

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