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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2024, Number 8, Pages 94–99
DOI: https://doi.org/10.26907/0021-3446-2024-8-94-99
(Mi ivm10009)
 

Approximation of positive solutions of symmetric eigenvalue problems with nonlinear dependence on the spectral parameter

P. S. Solov'ev

Kazan Federal University, 18 Kremlevskaya str., Kazan, 420008 Russia
References:
Abstract: A symmetric partial differential eigenvalue problem with nonlinear dependence on the spectral parameter arising in plasma physics is studied. We propose and justify new conditions for the existence of a positive eigenvalue and the corresponding positive eigenfunction. A finite element approximation of the problem preserving the property of positivity of solutions is constructed. The existence and convergence of approximate solutions are established.
Keywords: eigenvalue, positive eigenfunction, eigenvalue problem, finite element method.
Received: 03.04.2024
Revised: 03.04.2024
Accepted: 26.06.2024
Document Type: Article
UDC: 519.63
Language: Russian
Citation: P. S. Solov'ev, “Approximation of positive solutions of symmetric eigenvalue problems with nonlinear dependence on the spectral parameter”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 8, 94–99
Citation in format AMSBIB
\Bibitem{Sol24}
\by P.~S.~Solov'ev
\paper Approximation of positive solutions of symmetric eigenvalue problems with nonlinear dependence on the spectral parameter
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2024
\issue 8
\pages 94--99
\mathnet{http://mi.mathnet.ru/ivm10009}
\crossref{https://doi.org/10.26907/0021-3446-2024-8-94-99}
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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