Resumen de On the number of positive solutions of singularly perturbed 1D NLS

Patricio Luis Felmer Aichele, Salomé Martínez, Kazunaga Tanaka

• We study singularly perturbed 1D nonlinear Schrödinger equations (\ref{eq:1.1}). When $V(x)$ has multiple critical points, (\ref{eq:1.1}) has a wide variety of positive solutions for small $\varepsilon$ and the number of positive solutions increases to $\infty$ as $\varepsilon\to 0$. We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of $V(x)$. Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.