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We study the dipolar Gross-Piteavskii functional with the Lee-Huang-Yang(LHY) correction term without trapping potential and in the regime where thedipole-dipole interaction dominates the repulsive short-range interaction. Weshow that, above a critical mass, the functional admits minimizers and we provetheir regularity and exponential decay. We also estimate the critical mass interms of the parameters of the system.

Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction