Asymptotic behavior and monotonicity of radial eigenvalues for the p-Laplacian

We study the radial eigenvalues of the p-Laplacian in a domain ? with the Dirichlet boundary condition, where ? is a ball or an annulus. For the k-th eigenvalue lambda k(p, ?), we study the asymptotic behavior of lambda k(p, ?) as p -> 1 + 0 or p -> infinity, and prove the monotonicity and non-monotonicity of lambda k(p, ?) with respect to p. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).