In the following decades, researchers expanded on these foundational results. Thomas Bartsch and Sébastien de Valeriola investigate the existence of multiple normalized solutions to nonlinear Schrödinger equations. The authors focus on finding solutions that satisfy a prescribed L 2 norm constraint. Recent advancements include the study of normalized ground states for NLS equations with combined nonlinearities by Nicola Soave in 2020, who examined both subcritical and critical cases. This research highlighted the intricate balance between different types of nonlinearities and their impact on the existence and multiplicity of solutions.