Inserted: 31 jul 2006
Last Updated: 4 nov 2008
Journal: Proceedings of the Royal Society of Edinburgh
We study the asymptotic behavior of two nonlinear eigenvalue problems which involve $p$-Laplacian type operators. In the first problem we consider the limit as $p \to \infty$ of the sequences of the $k$-th eigenvalues of the $p-$Laplacian operators. The second problem we study is the homogenization of nonlinear eigenvalue problems for some $p$-Laplacian type operators with $p$ fixed. Our asymptotic analysis relies on a convergence result for particular critical values of a class of Rayleigh quotients, stated in a unified framework, and on the notion of $\Gamma$-convergence.
Keywords: Homogenization, Non-linear eigenvalues, $p$-Laplacian, $\infty$-eigenvalue problems