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| Ground States of K-component Coupled Nonlinear Schrodinger Equations with Inverse-square Potential* |
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Citation： |
Peng CHEN,Huimao CHEN,Xianhua TANG.Ground States of K-component Coupled Nonlinear Schrodinger Equations with Inverse-square Potential*[J].Chinese Annals of Mathematics B,2022,43(3):319~342 |
| Page view： 802
Net amount： 857 |
Authors： |
Peng CHEN; Huimao CHEN;Xianhua TANG |
Foundation： |
Natural Science Foundation of Hubei Province of China(No. 2021CFB473) and Hubei Educational Committee (No. D20161206). |
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| Abstract： |
In this paper, the authors study ground states for a class of K-component coupled nonlinear Schr¨odinger 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 ZN -translation invariance,many effective methods for periodic problems cannot be applied to asymptotically periodic ones. The third difficulty is singular potential μi/|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. |
Keywords： |
Schr¨odinger equations, Ground states, Strongly indefinite functionals,Non-Nehari manifold method. |
Classification： |
35J10, 35J20, 58E05 |
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