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, p. 508-521

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 : https://doi.org/10.1051/cocv:2005017
Classification:  35B40,  35J65
Keywords: eigenvalues, L -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},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {4},
     year = {2005},
     pages = {508-521},
     doi = {10.1051/cocv:2005017},
     zbl = {1103.35032},
     mrnumber = {2167872},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/COCV_2005__11_4_508_0/

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