Displaying similar documents to “Existence and multiplicity results for some weakly nonlinear elliptic problems at resonance”

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

Dimitri Mugnai (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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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.