EIGENVALUE HOMOGENISATION PROBLEM WITH INDEFINITE WEIGHTS
Julián Fernández Bonder, Juan Pablo Pinasco, Ariel Martin Salort · Bulletin of the Australian Mathematical Society · 2015
In this work we study the homogenisation problem for nonlinear elliptic equations involving $p$ -Laplacian-type 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 $k$ th positive eigenvalue goes to infinity when the average of the weights is nonpositive, and converges to the $k$ th variational eigenvalue of the limit problem when the average is positive for any $k\geq 1$ .