Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 64, pp. 122.
Weighted eigenvalue problems for the pLaplacian with
weights in weak Lebesgue spaces
T. V. Anoop
Abstract:
We consider the nonlinear eigenvalue problem
where
is the pLaplacian operator,
is a connected domain in
with
and the weight
function g is locally integrable. We obtain the existence
of a unique positive principal eigenvalue for g such
that
lies in certain subspace of weak
.
The radial symmetry of the first eigenfunctions are obtained for
radial g, when
is a ball centered at the origin or
.
The existence of an infinite set of eigenvalues
is proved using the LjusternikSchnirelmann theory on
manifolds.
Submitted November 11, 2010. Published May 17, 2011.
Math Subject Classifications: 35J92, 35P30, 35A15.
Key Words: Lorentz spaces; principal eigenvalue; radial symmetry;
LjusternikSchnirelmann theory.
Show me the PDF file (360 KB),
TEX file, and other files for this article.

T. V. Anoop
The Institute of Mathematical Sciences
Chennai 600113, India
email: tvanoop@imsc.res.in

Return to the EJDE web page