Analysis reveals a threshold phenomenon for existence of minimizers in two-dimensional nonlinear Schrödinger equations, indicating optimal constants in inequalities.
We consider the variational problem with a mass constraint arising from the two-dimensional dispersion managed nonlinear Schrödinger equation with power-law type nonlinearity. We prove a threshold phenomenon with respect to mass for the existence of minimizers for all possible powers of nonlinearities, including at the threshold itself. This threshold is closely related to the best constant for the Gagliardo-Nirenberg-Strichartz type inequality whose extremizers are found as a byproduct.
No takes yet. Share an insight, caveat, or question.
Choi et al. (2025) studied this question.
Synapse has enriched 2 closely related papers on similar clinical questions. Consider them for comparative context: