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
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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},
     pages = {195--215},
     year = {2006},
     volume = {8},
     number = {2},
     doi = {10.4171/jems/47},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/47/}
}
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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

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