Asymmetric elliptic problems with indefinite weights
by
Jean-Pierre Gossez
Universite Libre de Bruxelles
Coauthors: M.Arias, J.Campos, M.Cuesta

We prove the existence of a first nontrivial eigenvalue for the following asymmetric elliptic problem

ì í î -\Deltap u = \lambda[ m(x) (u+)p-1-n(x)(u-)p-1] in \Omega, u=0 on \partial\Omega.

A first application is given to the description of the beginning of the Fucik spectrum with weights for the p-laplacian. Another application concerns the study of nonresonance for the problem

ì í î -\Deltap u = f(x, u) in \Omega, u = 0 on \partial\Omega.

One feature of our nonresonance conditions is that they involve eigenvalues with weights rather that pointwise restrictions. (Joint work with M. Arias, J. Campos and M. Cuesta).

Date received: February 7, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-16.