| Abstract: |
| In this talk, I will present our recent results on bound state solutions for the coupled nonlinear elliptic system featuring both attractive and repulsive couplings. These solutions can be characterized as ground states within the subspace of even symmetric functions, whereas it is known that ground states do not exist in the full space of Sobolev functions. This scenario is referred to as the `repulsive-mixed case` according to the recent classification by Wei and Wu (J. Math. Pures Appl., 141:50-88, 2020), which established the non-existence of ground states for small attractive coupling. We extend this non-existence to all cases. This talk is based on the joint work with Professor Yohei Sato from Saitama University, Japan and Professor Zhi-Qiang Wang from Utah State University, USA. |
|