Electronic Journal of Differential Equations,
Conf. 10 (2002), pp. 251-256.

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

Author: Stephen B. Robinson (Wake Forest Univ., Winston-Salem, NC, USA)
 
Abstract: 
 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.
Math Subject Classifications: 35P30, 35J20, 35J65.
Key Words: Nonlinear eigenvalue problem; $p$-Laplacian; variational methods.