Semiclassical states for weakly coupled nonlinear Schr\"odinger systems

TL;DR

This paper investigates the existence and concentration behavior of nonnegative solutions in weakly coupled nonlinear Schrödinger systems with variable potentials, focusing on conditions for solutions to localize around potential minima.

Contribution

It provides new necessary and sufficient conditions for solution concentration in coupled Schrödinger systems with nonconstant potentials.

Findings

Solutions concentrate around local minima of potentials.

Established conditions for least energy solutions to localize.

Analyzed weakly coupled Schrödinger equations with variable potentials.

Abstract

We consider systems of weakly coupled Schr\"odinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.