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

Published online by Cambridge University Press:  15 September 2005

Dimitri Mugnai
Dimitri Mugnai*
Affiliation:
Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Perugia, Italy; mugnai@dipmat.unipg.it
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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$L^\infty-H_0^1$ estimatenodal linessymmetries.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 4 , October 2005 , pp. 508 - 521
Copyright
© EDP Sciences, SMAI, 2005

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