MONOTONICITY OF THE PRINCIPAL EIGENVALUE OF THE p-LAPLACIAN ON AN ANNULUS

Let D > 1 be a positive integer. For each real numbers a and b such that 0 < a < b < infinity consider the annulus A(a, b) := {x is an element of R-D : a < vertical bar x vertical bar < b}. Our goal is to give sufficient conditions on a and b such that the function which gives the principal eigenvalue of the p-Laplacian on A(a, b), subject to the homogeneous Dirichlet boundary condition, be monotone or non-monotone with respect to p is an element of (1 , infinity).