Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2002, pp. 251-156.

On the average value for nonconstant eigenfunctions of the p-Laplacian assuming Neumann boundary data

Stephen B. Robinson

We show that nonconstant eigenfunctions of the p-Laplacian do not necessarily have an average value of 0, as they must when p=2. This fact has implications for deriving a sharp variational characterization of the second eigenvalue for a general class of nonlinear eigenvalue problems.

Published February 28, 2003.
Subject classifications: 35P30, 35J20, 35J65.
Key words: Nonlinear eigenvalue problem, p-Laplacian, variational methods.

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Stephen B. Robinson
Department of Mathematics
Wake Forest University
Winston-Salem, NC 27109, USA

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