Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity results for a quasilinear equation with singular
  nonlinearity   For an open, bounded domain $\Om$ in $\mathbb{R}^N$ which is strictly convex
with $C^2$ boundary, we show that there exists a $\land>0$ such that the
singular quasilinear problem \begin{eqnarray*} &-\delp u
=\cfrac{\lambda}{u^{\del}}+u^q\,\,\mbox{in}\,\,\Om\\
&u=0\,\,\mbox{on}\,\,\partial\Om;\, \,\,u>0\,\,\mbox{in}\,\,\Om \end{eqnarray*}
admits atleast two solution $ u$ and $v$ in $W^{1,p}_{loc}(\Om)\cap
L^{\infty}(\Om)$ for any $\del>0$ and $0<\lam<\land$ provided $1<p<N$ and
$p-1<q<\frac{p(N-1)}{N-p}-1$.\\ Moreover the solutions $u$ and $v$ are such
that $u^{\alp}$ and $v^{\alp}$ are in $W^{1,p}_0(\Om)$ for some $\alp>0$.

3
The categories of this paper are: physics
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga