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.
Si studia l'esistenza di autovalori principali per operatori differenziali del secondo ordine non necessariamente in forma di divergenza. Otteniamo risultati sulla molteplicità degli autovalori principali, sia nel caso variazionale che per operatori in forma generale. Si utilizza sistematicamente il teorema di Krein-Rutman e poi un argomento di punto unito per il raggio spettrale di alcuni problemi ausiliari. La caratterizazione variazionale è usata nel caso auto-aggiunto e anche in quello generale.
@article{BUMI_2004_8_7B_1_159_0,
author = {J. Fleckinger and J. Hern\'andez and F. Th\'elin},
title = {Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {7-A},
year = {2004},
pages = {159-188},
zbl = {1117.35054},
mrnumber = {2044265},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_1_159_0}
}
Fleckinger, J.; Hernández, J.; Thélin, F. Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 159-188. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_1_159_0/
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