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; firstname.lastname@example.org
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 / estimate / nodal lines / symmetries.
© EDP Sciences, SMAI, 2005