Semiclassical Standing Waves with Clustering Peaks for Nonlinear Schrodinger Equations

The authors study the following singularly perturbed problem: $-\epsilon^2\Delta u+V(x)u = f(u)$ in $\mathbf{R}^N$. Their main result is the existence of a family of solutions with peaks that cluster near a local maximum of $V(x)$. A local variational and deformation argument in an infinite dimensional space is developed to establish the existence of such a family for a general class of nonlinearities $f$.