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

Berestycki, 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 -