Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and multiplicity for elliptic problems with quadratic growth
  in the gradient   We show that a class of divergence-form elliptic problems with quadratic
growth in the gradient and non-coercive zero order terms are solvable, under
essentially optimal hypotheses on the coefficients in the equation. In
addition, we prove that the solutions are in general not unique. The case where
the zero order term has the opposite sign was already intensively studied and
the uniqueness is the rule.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat