| Issue |
ESAIM: COCV
Volume 11, Number 4, October 2005
|
|
|---|---|---|
| Page(s) | 508 - 521 | |
| DOI | https://doi.org/10.1051/cocv:2005017 | |
| Published online | 15 September 2005 | |
Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue
Dipartimento di Matematica e
Informatica, Università di Perugia, via Vanvitelli 1, 06123
Perugia, Italy; mugnai@dipmat.unipg.it
Received:
30
March
2004
Revised:
30
November
2004
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.
Mathematics Subject Classification: 35B40 / 35J65
Key words: Eigenvalues / L∞−H01 estimate / nodal lines / symmetries.
© EDP Sciences, SMAI, 2005
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