Ground states for a nonlocal mixed order cubic-quartic Gross-Pitaevskii equation

We prove existence and qualitative properties of ground state solutions to a generalized nonlocal 3rd-4th order Gross-Pitaevskii equation. Using a mountain pass argument on spheres and constructing appropriately localized Palais-Smale sequences we are able to prove existence of real positive ground states as saddle points. The analysis is deployed in the set of possible states, thus overcoming the problem that the energy is unbounded below. We also prove a corresponding nonlocal Pohozaev identity with no rest term, a crucial part of the analysis. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper establishes the existence and qualitative properties of ground state solutions to a generalized nonlocal 3rd-4th order Gross-Pitaevskii equation. By utilizing a mountain pass argument on spheres and constructing appropriately localized Palais-Smale sequences, the existence of real positive ground states as saddle points is proven. Additionally, a nonlocal Pohozaev identity with no rest term is also demonstrated, which is a crucial part of the analysis.