Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient estimates for a nonlinear elliptic equation on complete
  Riemannian manifolds   In this short note, we consider gradient estimates for positive solutions to
the following nonlinear elliptic equation on a complete Riemannian manifold:
$$\Delta u+cu^{\alpha}=0,$$ where $c, \alpha$ are two real constants and $c\neq
0$.

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph