Single--peaks for a magnetic Schr\"{o}dinger equation with critic al growth

TL;DR

This paper establishes the existence of complex solutions for a magnetic Schrödinger equation with critical growth, using advanced critical point theory and perturbation methods.

Contribution

It introduces a novel approach to find solutions to a critical growth Schrödinger equation under electromagnetic perturbations.

Findings

Existence of complex solutions proven

Solutions are obtained via an abstract perturbation approach

Results extend understanding of Schrödinger equations with critical growth

Abstract

We prove existence results of complex-valued solutions for a semilinear Schr\"odinger equation with critical growth under the perturbation of an external electromagnetic field. Solutions are found via an abstract perturbation result in critical point theory.