Geodesic
Existence of positive solutions of symmetric variational eigenvalue problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2024), pp. 77-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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A symmetric variational eigenvalue problem in the Hilbert space with a cone is investigated. New sufficient conditions on the bilinear forms, the Hilbert space, and the cone of the variational problem guaranteeing the existence of a unique normalized positive eigenelement corresponding to a positive simple minimal eigenvalue are proposed and justified. The obtained abstract results are illustrated by the example of the generalized eigenvalue problem for the second order self-adjoint elliptic differential operator.
Keywords: eigenvalue, symmetric eigenvalue problem, Hilbert space, cone, self-adjoint elliptic differential operator, maximum principle, positive eigenfunction.
Mots-clés : eigenelement 
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P. S. Solov'ev. Existence of positive solutions of symmetric variational eigenvalue problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2024), pp. 77-84. http://geodesic.mathdoc.fr/item/IVM_2024_7_a6/

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