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Ground States of K-component Coupled Nonlinear Schrödinger Equations with Inverse-square Potential

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Abstract

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 ℤN-translation invariance, many effective methods for periodic problems cannot be applied to asymptotically periodic ones. The third difficulty is singular potential \({{{\mu _i}} \over {{{\left| x \right|}^2}}}\), 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.

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Acknowledgement

The authors would like to thank the anonymous reviewers for thelp and thoughtful suggestions that have helped to improve this paper substantially.

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Authors and Affiliations

  1. Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei, 443002, China

    Peng Chen

  2. College of Science, China Three Gorges University, Yichang, Hubei, 443002, China

    Huimao Chen

  3. School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, China

    Peng Chen & Xianhua Tang

Authors
  1. Peng Chen
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  2. Huimao Chen
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  3. Xianhua Tang
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Corresponding authors

Correspondence to Peng Chen, Huimao Chen or Xianhua Tang.

Additional information

This work was supported by the Natural Science Foundation of Hubei Province of China (No. 2021CFB473) and Hubei Educational Committee (No. D20161206).

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Chen, P., Chen, H. & Tang, X. Ground States of K-component Coupled Nonlinear Schrödinger Equations with Inverse-square Potential. Chin. Ann. Math. Ser. B 43, 319–342 (2022). https://doi.org/10.1007/s11401-022-0325-6

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  • DOI: https://doi.org/10.1007/s11401-022-0325-6

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