Existence of standing waves solution for a Nonlinear Schrödinger equations in $\mathbb{R}^{N}$

In this paper, we investigate the existence of positive solution for the following class of elliptic equation $$ - ε^{2}Δu +V(x)u= f(u) \,\,\,\, \mbox{in} \,\,\, \mathbb{R}^{N}, $$ where $ε>0$ is a positive parameter, $f$ has a subcritical growth and $V$ is a positive potential verifying some conditions.

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