Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains
Denis Borisov, Pedro Freitas (2009)
Annales de l'I.H.P. Analyse non linéaire
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Denis Borisov, Pedro Freitas (2009)
Annales de l'I.H.P. Analyse non linéaire
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Veliev, O.A. (2009)
Abstract and Applied Analysis
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Eberhard, W., Freiling, G., Schneider, A. (1992)
International Journal of Mathematics and Mathematical Sciences
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O. A. Olejnik (1989)
Journées équations aux dérivées partielles
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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.
Nazarov, Serguei A.
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Jan Bochenek (1971)
Annales Polonici Mathematici
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