T. V. Anoop
We consider the nonlinear eigenvalue problem
where is the p-Laplacian 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 Ljusternik-Schnirelmann 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; Ljusternik-Schnirelmann theory.
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| T. V. Anoop |
The Institute of Mathematical Sciences
Chennai 600113, India
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