Note on a paper of E. M. E. Zayed and S. F. M. Ibraham.
Eberhard, W., Freiling, G., Schneider, A. (1992)
International Journal of Mathematics and Mathematical Sciences
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Eberhard, W., Freiling, G., Schneider, A. (1992)
International Journal of Mathematics and Mathematical Sciences
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Yan, Ping (2010)
Boundary Value Problems [electronic only]
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Dorin Bucur (2005)
Control and Cybernetics
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Serguei Nazarov, Jan Sokołowski (2008)
Control and Cybernetics
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J. Fleckinger, J. Hernández, F. Thélin (2004)
Bollettino dell'Unione Matematica Italiana
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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
Julián Fernández Bonder, Julio D. Rossi (2002)
Publicacions Matemàtiques
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In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end...
Édouard Oudet (2004)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.