Normalized Solutions to Schr\"{o}dinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach
Analysis of PDEs
2024-09-17 v1
Abstract
We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schr\"{o}dinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass supercritical, critical, subcritical or some mixes of these cases, and the equation can be autonomous or non-autonomous. This generalizes a result in Noris, Tavares and Verzini [\emph{Anal. PDE}, 7 (8) (2014) 1807-1838], where the equation is autonomous with homogeneous nonlinearities. Besides, we have proven some orbital stability or instability results.
Keywords
Cite
@article{arxiv.2409.10299,
title = {Normalized Solutions to Schr\"{o}dinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach},
author = {Wei Ji},
journal= {arXiv preprint arXiv:2409.10299},
year = {2024}
}