Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The first eigenvalue and eigenfunction of a nonlinear elliptic system   In this paper, we study the first eigenvalue of a nonlinear elliptic system
involving $p$-Laplacian as the differential operator. The principal eigenvalue
of the system and the corresponding eigenfunction are investigated both
analytically and numerically. An alternative proof to show the simplicity of
the first eigenvalue is given. In addition, the upper and lower bounds of the
first eigenvalue are provided. Then, a numerical algorithm is developed to
approximate the principal eigenvalue. This algorithm generates a decreasing
sequence of positive numbers and various examples numerically indicate its
convergence. Further, the algorithm is generalized to a class of gradient
quasilinear elliptic systems.

25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int