On the Ground States of Spin‐2 Bose‐Einstein Condensates Without External Potentials in ℝ3

ABSTRACT In this paper, we study the ground states of spin‐2 Bose‐Einstein condensates in with spin‐independent interaction constant and spin‐exchange interaction constant . Two conserved quantities are involved: the number of atoms and the total magnetization . We mainly investigate the existence and strong instability of ground‐state standing waves in the case of no external potential. The bounded Palais‐Smale sequence satisfying the Pohozaev identity in the limit sense is obtained by a minimax theorem. Applying the technique of mass‐redistribution, we further determine the signs of corresponding Lagrange multipliers, which allows the strong convergence of the approximate critical point sequence in . Our method presents an alternative proof for excluding semi‐trivial solutions already available in some literature.