Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic variational problems with mixed nonlinearities   In this paper, we study the existence and multiplicity results of nontrivial
positive solutions to a quasilinear elliptic equation in $\RN$, when $N\geq2$,
as \begin{equation} \Lp
u+u^{p-1}=\lambda\hspace{0.2mm}k(x)u^{r-1}-h(x)u^{q-1}.\nonumber \end{equation}
Here, $h(x),k(x)>0$ are Lebesgue measurable functions, $1<p<q<\infty$,
$p<r<\min\{p^*,q\}$ if $p<N$ while $p<r<q$ if $p\geq N$, and $\lambda>0$ is a
parameter.

5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio