Abstract: In this paper, we study solution structures of the following generalized Lennard-Jones systems in Rn. Considering periodic solutions with zero angular momentums, we prove that the corresponding problem degenerates to 1-dimensional and possesses in nitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentums, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. Then we further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions. This is a joint work with Professor Yiming Long and Professor Chongchun Zeng.
