Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Meromorphic solutions of delay differential equations related to
  logistic type and generalizations   Let $\{b_{j}\}_{j=1}^{k}$ be meromorphic functions, and let $w$ be admissible
meromorphic solutions of delay differential equation
$$w'(z)=w(z)\left[\frac{P(z,
w(z))}{Q(z,w(z))}+\sum_{j=1}^{k}b_{j}(z)w(z-c_{j})\right]$$ with distinct
delays $c_{1}, \ldots, c_{k}\in\mathbb{C}\setminus\{0\},$ where the two nonzero
polynomials $P(z, w(z))$ and $Q(z, w(z))$ in $w$ with meromorphic coefficients
are prime each other. We obtain that if $\limsup_{r\rightarrow\infty}\frac{\log
T(r, w)}{r}=0,$ then $$deg_{w}(P/Q)\leq k+2.$$ Furthermore, if $Q(z, w(z))$ has
at least one nonzero root, then $deg_{w}(P)=deg_{w}(Q)+1\leq k+2;$ if all roots
of $Q(z, w(z))$ are nonzero, then $deg_{w}(P)=deg_{w}(Q)+1\leq k+1;$ if
$deg_{w}(Q)=0,$ then $deg_{w}(P)\leq 1.$\par
  In particular, whenever $deg_{w}(Q)=0$ and $deg_{w}(P)\leq 1$ and without the
growth condition, any admissible meromorphic solution of the above delay
differential equation (called Lenhart-Travis' type logistic delay differential
equation) with reduced form can not be an entire function $w$ satisfying
$\overline{N}(r, \frac{1}{w})=O(N(r, \frac{1}{w}));$ while if all coefficients
are rational functions, then the condition $\overline{N}(r, \frac{1}{w})=O(N(r,
\frac{1}{w}))$ can be omitted. Furthermore, any admissible meromorphic solution
of the logistic delay differential equation (that is, for the simplest special
case where $k=1$ and $deg_{w}(P/Q)=0$ ) satisfies that $N(r,w)$ and $T(r, w)$
have the same growth category. Some examples support our results.

22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ
1
The categories of this paper are: cs