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Approximation of nonlinear spectral problems in a Hilbert space

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Abstract

We study an eigenvalue problem with a nonlinear dependence on the parameter in a Hilbert space. We establish the existence of eigenvalues and eigenelements. The original infinite-dimensional problem is approximated by a problem in a finite-dimensional subspace. We investigate the convergence and accuracy of approximate eigenvalues and eigenelements.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, Kazan, Russia

    S. I. Solov’ev

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  1. S. I. Solov’ev
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Correspondence to S. I. Solov’ev.

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Original Russian Text © S.I. Solov’ev, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 7, pp. 937–950.

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Solov’ev, S.I. Approximation of nonlinear spectral problems in a Hilbert space. Diff Equat 51, 934–947 (2015). https://doi.org/10.1134/S0012266115070113

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