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

Published online by Cambridge University Press:  15 September 2005

Dimitri Mugnai*
Affiliation:
Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Perugia, Italy; [email protected]
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Abstract

We give the precise behaviour of some solutions of a nonlinearelliptic B.V.P. in a bounded domain when a parameter approaches aneigenvalue of the principal part. If the nonlinearity has someregularity and the domain is for example convex, we also prove anonlinear version of Courant's Nodal theorem.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2005

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