  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.
