Eigenvalue homogenisation problem with indefinite weights

Abstract

In this work we study the homogenisation problem for nonlinear elliptic equations involving p-Laplaciantype operators with sign-changing weights. We study the asymptotic behaviour of variational eigenvalues which consist of a double sequence of eigenvalues. We show that the kth positive eigenvalue goes to infinity when the average of the weights is nonpositive, and converges to the kth variational eigenvalue of the limit problem when the average is positive for any k ≥ 1.