Precise asymptotic of eigenvalues of resonant quasilinear systems

Details Precise asymptotic of eigenvalues of resonant quasilinear systems Precise asymptotic of eigenvalues of resonant quasilinear systems

2008-11-10

arxiv.org/abs/0811.1542v2

Mathematics

Analysis of PDEs

Minor changes, Theorem 1.4 added

Scientific paper

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 $\alpha+\beta$, $\lam_k = O(k^{\frac{\alpha+\beta}{N}})$.

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