  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.
