Geodesic
Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 508-521

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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.

DOI : 10.1051/cocv:2005017
Classification : 35B40, 35J65
Keywords: eigenvalues, $L^\infty -H_0^1$ estimate, nodal lines, symmetries 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv:2005017/}
}
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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, Tome 11 (2005) no. 4, pp. 508-521. doi: 10.1051/cocv:2005017

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