Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comparison estimates on the first eigenvalue of a quasilinear elliptic
  system   We study a system of quasilinear eigenvalue problems with Dirichlet boundary
conditions on complete compact Riemannian manifolds. In particular, Cheng
comparison estimates and inequality of Faber-Krahn for the first eigenvalue of
a $(p,q)$-Laplacian are recovered. Lastly, we reprove a Cheeger type estimates
for $p$-Laplacian, $1<p<\infty$, from where a lower bound estimate in terms of
Cheeger's constant for the first eigenvalue of a $(p,q)$-Laplacian is built. As
a corollary, the first eigenvalue converges to Cheeger's constant as $p,q\to
1,1.$

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The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con