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.
Guo et al. (Wed,) studied this question.