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 Ω⊂RN, with a coupling term depending on two parameters α and β satisfying α/p+β/q=1. We show that the order of growth of the kth eigenvalue depends on α+β, λk=O(k α+β/N).