ON THE STRUCTURE OF THE SECOND EIGENFUNCTIONS OF THE p-LAPLACIAN ON A BALL.

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. [ABSTRACT FROM AUTHOR]