Electron. J. Diff. Eqns., Vol. 2001(2001), No. 33, pp. 19.
Eigenvalue problems for the pLaplacian with indefinite weights
Mabel Cuesta
Abstract:
We consider the eigenvalue problem
where
,
is the pLaplacian 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, pLaplacian, indefinite weight.
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Mabel Cuesta
Universite du Littoral
ULCO, 50, rue F. Buisson,
B.P. 699, F62228 Calais, France
email: cuesta@lmpa.univlittoral.fr 
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