Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Principal eigenvalues of a class of nonlinear integro-differential
  operators   We consider a class of nonlinear integro-differential operators and prove
existence of two principal (half) eigenvalues in bounded smooth domains with
exterior Dirichlet condition. We then establish simplicity of the principal
eigenfunctions in viscosity sense, maximum principles, continuity property of
the principal eigenvalues with respect to domains etc. We also prove an
anti-maximum principle and study existence result for some nonlinear problem
via Rabinowitz bifurcation-type results.

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The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat