Semiclassical analysis of low lying eigenvalues. I. Non-degenerate minima : asymptotic expansions
Barry Simon (1983)
Annales de l'I.H.P. Physique théorique
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Barry Simon (1983)
Annales de l'I.H.P. Physique théorique
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Xue Ping Wang (2007)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
M. Klaus (1981)
Annales de l'I.H.P. Physique théorique
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O. A. Olejnik (1989)
Journées équations aux dérivées partielles
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Jan Bochenek (1990)
Annales Polonici Mathematici
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Milutin Dostanić (1996)
Matematički Vesnik
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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.