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.

Keywords: eigenvalues, $L^\infty -H_0^1$ estimate, nodal lines, symmetries

@article{COCV_2005__11_4_508_0, author = {Mugnai, Dimitri}, title = {Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {508--521}, publisher = {EDP-Sciences}, volume = {11}, number = {4}, year = {2005}, doi = {10.1051/cocv:2005017}, mrnumber = {2167872}, zbl = {1103.35032}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2005017/} }

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 PY - 2005 SP - 508 EP - 521 VL - 11 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2005017/ DO - 10.1051/cocv:2005017 LA - en ID - COCV_2005__11_4_508_0 ER -

%0 Journal Article %A Mugnai, Dimitri %T Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 508-521 %V 11 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2005017/ %R 10.1051/cocv:2005017 %G en %F COCV_2005__11_4_508_0

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, Volume 11 (2005) no. 4, pp. 508-521. doi : 10.1051/cocv:2005017. http://archive.numdam.org/articles/10.1051/cocv:2005017/

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