Stationary solutions of the nonlinear Schrödinger equation with fast-decay potentials concentrating around local maxima

Abstract

We study positive bound states for the equation $$-{\epsilon }^2\Delta u+Vu=u^p,\text{in RN},$$ where $\epsilon >0$ is a real parameter, $\frac{N}{N-2}<p<\frac{N+2}{N-2}$ and $V$ is a nonnegative potential. Using purely variational techniques, we find solutions which concentrate at local maxima of the potential $V$ without any restriction on the potential.

25 pages, reformatted the abstract for MathJax