Asymptotic behaviour of nonlinear eigenvalue problems involving $p$-Laplacian-type operators
Thierry Champion, Luigi De Pascale · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2007
We study the asymptotic behaviour 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 $\varGamma$ -convergence.