Semiclassical states of nonlinear Schrödinger equations with bounded potentials (Q1357120)

Summary: Using some perturbation results in critical point theory, we prove that a class of nonlinear Schrödinger equations \[ i\hslash {\partial\psi\over\partial t}= -\hslash^2\Delta\psi+ V(x)\psi-|\psi|^{p-1}\psi,\quad x\in\mathbb{R}^N, \] possesses semiclassical states that concentrate near the critical points of the potential \(V\).