Published Paper

Inserted: 7 nov 2007

Journal: ESAIM:COCV
Volume: 11
Number: 4
Pages: 508-521
Year: 2005

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.

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

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