Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic solutions for indefinite singular equations with applications
  to the weak case   As a consequence of the main result of this paper efficient conditions
guaranteeing the existence of a $T-$periodic solution to the second order
differential equation \begin{equation*} u"=\frac{h(t)}{u^{\lambda}}
\end{equation*} are established. Here, $h\in L(\mathbb{R}/T\mathbb{Z})$ is a
piecewise-constant sign-changing function where the non-linear term presents a
weak singularity at 0 (i.e. $\lambda\in (0,1)$).

16
The categories of this paper are: stat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an