On Decay of Solutions to Gross–Pitaevskii Systems

We investigate the existence and decay properties of solutions to the following elliptic systems, which arise in the context of Bose–Einstein condensation: [Formula: see text] To analyze the decay behavior of solutions, we use a variant of Moser’s iteration technique, with general conditions imposed on the potentials [Formula: see text] and [Formula: see text]. Our results extend recent findings by Angeles, Clapp, and Saldaña (2023). We pay particular attention to potential classes that either vanish or are unbounded at infinity. The existence of ground states is established under these assumptions, and the derived decay estimates are also used to show that weak solutions exhibit either exponential or polynomial decay.