摘要
In this paper,the authors study ground states for a class of K-component coupled nonlinear Schrödinger equations with a sign-changing potential which is periodic or asymptotically periodic.The resulting problem engages three major difficulties:One is that the associated functional is strongly indefinite,the second is that,due to the asymptotically periodic assumption,the associated functional loses the Z^(N)-translation invariance,many effective methods for periodic problems cannot be applied to asymptotically periodic ones.The third difficulty is singular potentialμ/(|x|)^(2),which does not belong to the Kato’s class.These enable them to develop a direct approach and new tricks to overcome the difficulties caused by singularity and the dropping of periodicity of potential.
基金
supported by the Natural Science Foundation of Hubei Province of China(No.2021CFB473)
Hubei Educational Committee(No.D20161206)