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On the structure of the second eigenfunctions of the p-laplacian on a ball
T.V. Anoop, P. Drábek,
Published in American Mathematical Society
2016
Volume: 144
   
Issue: 6
Pages: 2503 - 2512
Abstract
In this paper, we prove that the second eigenfunctions of the p- Laplacian, p > 1, are not radial on the unit ball in RN, for any N ≥ 2. Our proof relies on the variational characterization of the second eigenvalue and a variant of the deformation lemma. We also construct an infinite sequence of eigenpairs {τn,Ψn} such that Ψn is nonradial and has exactly 2n nodal domains. A few related open problems are also stated. © 2015 American Mathematical Society.
About the journal
JournalProceedings of the American Mathematical Society
PublisherAmerican Mathematical Society
ISSN00029939