Three bound states with prescribed angular momentum to the cubic-quintic NLS equations in ℝ³

2025/07/05 by Yao, Shuai, Sun, Juntao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.04057

Abstract

In this paper, we investigate bound states with prescribed angular momentum and mass for the nonlinear Schrödinger equations (NLS) with the cubic-quintic nonlinearity in dimensions three. We demonstrate that there exist three solutions for the double constrained problem: a local minimizer, a mountain pass type solution, and a global minimizer. Moreover, by means of the minimax method, we construct a new mountain pass path and further obtain the geometric link among the three solutions as well as a comparison of their energy levels. This seems to be the first paper concerning three solutions, with the method also being applicable to the single constraint problem.

Citations

• Nonlinear bound states with prescribed angular momentum in the mass supercritical regime
• Nonlinear bound states with prescribed angular momentum
• Multiplicity, asymptotics and stability of standing waves for nonlinear Schrödinger equation with rotation
• Nonlinear Schr�dinger equations and sharp interpolation estimates

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