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

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

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

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topMugnai, 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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