Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Viewing nonoscillatory second order linear differential equations from
  the angle of Riccati equations   We build an existence theory for nonoscillatory second order differential
equations of the form (A) $(p(t)x')' = q(t)x, $ $p(t)$ and $q(t)$ being
positive continuous functions on $[a,\infty)$, in which a crucial role is
played by a pair of the Riccati differential equations (R1) $u' = q(t) -
u^2/p(t)$, (R2) $ v' = 1/p(t) - q(t)v^2$, associated with (A). An essential
part of the theory is the construction of a pair of linearly independent
nonoscillatory solutions $x_1(t)$ and $x_2(t)$ of (A) enjoying explicit
exponential-integral representations in terms of solutions $u_1(t)$ and
$u_2(t)$ of (R1) or in terms of solutions $v_1(t)$ and $v_2(t)$ of (R2).

30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat