Existence and multiplicity of positive solutions to a $p$-Laplacian equation in $\Bbb R^N$

In this work we study the existence, multiplicity and concentration of positive solutions for the following class of problem \begin{equation} - \epsilon^{p} \Delta_{p}u + V(z)|u|^{p-2}u=f(u), \,\,\, u(z) > 0, \forall \ z \in \mathbb R^N , \tag*{$(P_{\epsilon})$} \end{equation} where $\Delta_{p}u$ is the p-Laplacian operator, $\epsilon$ is a positive parameter, $2 \leq p < N, V:\mathbb R^N \to \mathbb R$ is a continuous functions and $f:\mathbb R \to \mathbb R$ is a function of $C^{1}$ class.