Symmetric Nonradial Solutions for Nonlinear Schrödinger Systems with Mixed Couplings on $\mathbb R$$^{\boldsymbol n}$

Source abstract

Abstract. For a coupled nonlinear elliptic system having both attractive and repulsive couplings involved we construct a nonradial bound state solution characterized as the ground state in the subspace of even symmetric functions while it is known that the ground state in the full space of Sobolev functions does not exist. This case is termed the repulsive-mixed case by the recent classification proposed in [J. Wei and Y. Wu, J. Math. Pures Appl. (9), 141 (2020), pp. 50–88] 38 in which the nonexistence of ground states was proved for small attractive coupling; we prove here the nonexistence of ground states for all cases. We analyze the asymptotic behavior of the solutions as the attractive coupling gets large, exhibiting a multiscaled asymptotic profile of the solution with the components at different orders of the energy levels.