Concentration of nodal solutions for semiclassical quadratic Choquard equations

Abstract

In this article concerns the semiclassical Choquard equation \(-\varepsilon^2 \Delta u +V(x)u = \varepsilon^{-2}( \frac{1}{|\cdot|}* u^2)u\) for \(x \in \mathbb{R}^3\) and small \(\varepsilon\). We establish the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function \(V\), by means of the perturbation method and the method of invariant sets of descending flow. For more information see https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html