  This paper deals with the existence of solutions for the following perturbed
Schr\"{o}dinger equation \begin{equation*} -\varepsilon^{2} \Delta u + V(x)u=
|u|^{p-2}u, \, \, \text{ in } \, \, \r^{N}, \end{equation*} where $\varepsilon$
is a parameter, $N \geq 3$, $p \in (2, \frac{2N}{N-2})$, and $V(x)$ is a
potential function in $\r^{N}$. We demonstrate an interesting ``dichotomy''
phenomenon for concentrating solutions of the above Schr\"{o}dinger equation.
More specifically, we construct infinitely many new solutions with peaks
locating both in the bounded domain and near infinity, which fulfills the
profile of the concentration compactness. Moreover, this approach can be
extended to solve other related problems.
