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

P. S. Solov'ev

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2024), pp. 94-99

Résumé

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.

Détail

Keywords: eigenvalue, positive eigenfunction, eigenvalue problem, finite element method.

Bibliographie

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