Eigenvalue homogenization problems with indefinite weights

JUAN PABLO PINASCO; JULIÁN FERNANDEZ BONDER; ARIEL SALORT

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY

AUSTRALIAN MATHEMATICS PUBL ASSOC INC

Año: 2016 vol. 93 p. 113 - 127

0004-9727

In this work we study the homogenization problem for nonlinear elliptic equations involving $p-$Laplacian type operators with sign changing weights. We study the asymptotic behavior of variational eigenvalues, which consist on a double sequence of eigenvalues. We show that the $k-$th positive eigenvalue goes to infinity when the average of the weight is nonpositive, and converge to the $k-$th variational eigenvalue of the limit problem when the average is positive for any $kge 1$.