Existence and Multiplicity of Normalized Solutions to Schr\"{o}dinger Equations with General Nonlinearities in Bounded Domains
Analysis of PDEs
2025-06-19 v2
Abstract
This paper focuses on the existence of multiple normalized solutions to Schr\"{o}dinger equations with general nonlinearities in bounded domains via variational methods. We first obtain two positive normalized solutions, one is a normalized ground state by searching for a local minimizer, and the other one is a mountain pass solution. Secondly, using a version of Linking theorems for normalized solutions, we prove the multiplicity of solutions to Schr\"{o}dinger equations in a star-shaped bounded domain. Moreover, we arrive at the existence of nonradial normalized solutions to Schr\"odinger equations in a ball.
Keywords
Cite
@article{arxiv.2409.15089,
title = {Existence and Multiplicity of Normalized Solutions to Schr\"{o}dinger Equations with General Nonlinearities in Bounded Domains},
author = {Wei Ji},
journal= {arXiv preprint arXiv:2409.15089},
year = {2025}
}