Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of a periodic solution for superlinear second order ODEs   We prove a necessary and sufficient condition for the existence of a
$T$-periodic solution for the time-periodic second order differential equation
$\ddot{x}+f(t,x)+p(t,x,\dot x)=0$, where $f$ grows superlinearly in $x$
uniformly in time, while $p$ is bounded. Our method is based on a fixed-point
theorem which uses the rotational properties of the dynamics.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ