Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue

Dimitri Mugnai

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 11, Issue: 4, page 508-521
  • ISSN: 1292-8119

Abstract

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We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant's Nodal theorem.

How to cite

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Mugnai, Dimitri. "Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue." ESAIM: Control, Optimisation and Calculus of Variations 11.4 (2010): 508-521. <http://eudml.org/doc/90775>.

@article{Mugnai2010,
abstract = { We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant's Nodal theorem. },
author = {Mugnai, Dimitri},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Eigenvalues; $L^\infty-H_0^1$ estimate; nodal lines; symmetries.; estimates; symmetries},
language = {eng},
month = {3},
number = {4},
pages = {508-521},
publisher = {EDP Sciences},
title = {Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue},
url = {http://eudml.org/doc/90775},
volume = {11},
year = {2010},
}

TY - JOUR
AU - Mugnai, Dimitri
TI - Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 11
IS - 4
SP - 508
EP - 521
AB - We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant's Nodal theorem.
LA - eng
KW - Eigenvalues; $L^\infty-H_0^1$ estimate; nodal lines; symmetries.; estimates; symmetries
UR - http://eudml.org/doc/90775
ER -

References

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