Geodesic
Approximation of positive solutions of symmetric eigenvalue problems with nonlinear dependence on the spectral parameter
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2024), pp. 94-99

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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. 
P. S. Solov'ev. Approximation of positive solutions of symmetric eigenvalue problems with nonlinear dependence on the spectral parameter. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2024), pp. 94-99. http://geodesic.mathdoc.fr/item/IVM_2024_8_a8/
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     title = {Approximation of positive solutions of symmetric eigenvalue problems with nonlinear dependence on the spectral parameter},
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