Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and multiplicity of solutions for a class of quasilinear
  elliptic field equation on $\mathbb{R}^{N}$   In this paper, we establish existence and multiplicity of solutions for the
following class of quasilinear field equation $$ -\Delta
u+V(x)u-\Delta_{p}u+W'(u)=0, \,\,\, \mbox{in} \,\,\, \mathbb{R}^{N}, \eqno{(P)}
$$ where $u=(u_1,u_2,...,u_{N+1})$, $p>N \geq 2$, $W$ is a singular function
and $V$ is a positive continuous function.

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an