Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entire solutions of fully nonlinear elliptic equations with a
  superlinear gradient term   In this paper we consider second order fully nonlinear operators with an
additive superlinear gradient term. Like in the pioneering paper of Brezis for
the semilinear case, we obtain the existence of entire viscosity solutions,
defined in all the space, without assuming global bounds. A uniqueness result
is also obtained for special gradient terms, subject to a convexity/concavity
type assumption where superlinearity is essential and has to be handled in a
different way from the linear case.

8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
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
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin