# On the principal eigenvalue of elliptic operators in ${\mathbb{R}}^{N}$ and applications

Journal of the European Mathematical Society (2006)

- Volume: 008, Issue: 2, page 195-215
- ISSN: 1435-9855

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topBerestycki, Henry, and Rossi, Luca. "On the principal eigenvalue of elliptic operators in $\mathbb {R}^N$ and applications." Journal of the European Mathematical Society 008.2 (2006): 195-215. <http://eudml.org/doc/277596>.

@article{Berestycki2006,

abstract = {Two generalizations of the notion of principal eigenvalue for elliptic operators in $\mathbb \{R\}^N$ 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.},

author = {Berestycki, Henry, Rossi, Luca},

journal = {Journal of the European Mathematical Society},

keywords = {elliptic operators; principal eigenvalue; generalized principal eigenvalue in $\mathbb \{R\}^N$; limit periodic operators; generalized principal eigenvalue; elliptic operator; smooth domain},

language = {eng},

number = {2},

pages = {195-215},

publisher = {European Mathematical Society Publishing House},

title = {On the principal eigenvalue of elliptic operators in $\mathbb \{R\}^N$ and applications},

url = {http://eudml.org/doc/277596},

volume = {008},

year = {2006},

}

TY - JOUR

AU - Berestycki, Henry

AU - Rossi, Luca

TI - On the principal eigenvalue of elliptic operators in $\mathbb {R}^N$ and applications

JO - Journal of the European Mathematical Society

PY - 2006

PB - European Mathematical Society Publishing House

VL - 008

IS - 2

SP - 195

EP - 215

AB - Two generalizations of the notion of principal eigenvalue for elliptic operators in $\mathbb {R}^N$ 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.

LA - eng

KW - elliptic operators; principal eigenvalue; generalized principal eigenvalue in $\mathbb {R}^N$; limit periodic operators; generalized principal eigenvalue; elliptic operator; smooth domain

UR - http://eudml.org/doc/277596

ER -

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