On the principal eigenvalue of elliptic operators in $\R^N$ and applications | Zendy

Henri Berestycki | Zendy; Luca Rossi | Zendy

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On the principal eigenvalue of elliptic operators in $\R^N$ and applications

Author(s) -

Henri Berestycki,

Luca Rossi

Publication year - 2006

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/47

Subject(s) - mathematics , elliptic operator , eigenvalues and eigenvectors , principal (computer security) , dimension (graph theory) , uniqueness , operator theory , pure mathematics , limit (mathematics) , semi elliptic operator , operator (biology) , mathematical analysis , algebra over a field , differential operator , physics , quantum mechanics , computer science , operating system , biochemistry , chemistry , repressor , transcription factor , gene

Two generalizations of the notion of principal eigenvalue for elliptic operators in R-N 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 semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures

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