Precise asymptotic of eigenvalues of resonant quasilinear systems

Abstract

In this work we study the sequence of variational eigenvalues of a system of resonant type involving $p-$ and $q-$laplacians on $\Omega \subset {\mathbb{R}}^N$, with a coupling term depending on two parameters $\alpha$ and $\beta$ satisfying $\alpha /p+\beta /q=1$. We show that the order of growth of the $k^{th}$ eigenvalue depends on $\alpha +\beta$, $\lam_k = O(k^{\frac{α+β}{N}})$.

arXiv commentMinor changes, Theorem 1.4 added