Precise asymptotic of eigenvalues of resonant quasilinear systems

• Main Authors: Bonder, J. Fernandez, Pinasco, J. P
• Format: Journal Article
• Language: English
• Published: 10-11-2008
• Subjects: Mathematics - Analysis of PDEs; Mathematics - Spectral Theory
• DOI: 10.48550/arxiv.0811.1542

In this work we study the sequence of variational eigenvalues of a system of
resonant type involving $p-$ and $q-$laplacians on $\Omega \subset \R^N$, 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 $\alpha+\beta$, $\lam_k = O(k^{\frac{\alpha+\beta}{N}})$.