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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
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
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
Linking options:
https://www.mathnet.ru/eng/ivm10009 https://www.mathnet.ru/eng/ivm/y2024/i8/p94
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Abstract page: | 72 | Full-text PDF : | 1 | References: | 9 | First page: | 3 |
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