Electron. J. Diff. Eqns., Vol. 2001(2001), No. 33, pp. 1-9.

### Eigenvalue problems for the p-Laplacian with indefinite weights Mabel Cuesta

Abstract:
We consider the eigenvalue problem

where , is the p-Laplacian operator, , is a bounded domain in and is a given function in ( depending on and ). The weight function may change sign and has nontrivial positive part. We prove that the least positive eigenvalue is simple, isolated in the spectrum and it is the unique eigenvalue associated to a nonnegative eigenfunction. Furthermore, we prove the strict monotonicity of the least positive eigenvalue with respect to the domain and the weight.

Submitted April 4, 2001. Published May 10, 2001.
Math Subject Classifications: 35J20, 35J70, 35P05, 35P30
Key Words: Nonlinear eigenvalue problem, p-Laplacian, indefinite weight.

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 Mabel Cuesta Universite du Littoral ULCO, 50, rue F. Buisson, B.P. 699, F-62228 Calais, France e-mail: cuesta@lmpa.univ-littoral.fr