Geodesic
On the principal eigenvalue of elliptic operators in $\R^N$ and applications
Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 195-215.

Voir la notice de l'article provenant de la source EMS Press

Two generalizations of the notion of principal eigenvalue for elliptic operators in RN are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semi-linear problems in all of space. We also indicate several outstanding open problems and formulate some conjectures.
DOI : 10.4171/jems/47
Classification : 35-XX, 00-XX
Keywords: Elliptic operators, principal eigenvalue, generalized principal eigenvalue in RN, limit periodic operators 
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     author = {Henri Berestycki and Luca Rossi},
     title = {On the principal eigenvalue of elliptic operators in $\R^N$ and applications},
     journal = {Journal of the European Mathematical Society},
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Henri Berestycki; Luca Rossi. On the principal eigenvalue of elliptic operators in $\R^N$ and applications. Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 195-215. doi : 10.4171/jems/47. http://geodesic.mathdoc.fr/articles/10.4171/jems/47/

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