Ground states for asymptotically linear fractional Schrödinger–Poisson systems

Abstract

In this paper we consider the following fractional Schrödinger–Poisson system

$$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^s u+u+K(x)\phi (x)u=g(x, u), \quad x\in \mathbb {R}^{3}, \\ (-\Delta )^s \phi =K(x)u^2, \quad x\in \mathbb {R}^{3}, \end{array}\right. } \end{aligned}$$

where \(s\in (\frac{1}{2},1)\) and g(xu) is asymptotically linear at infinity. Under certain assumptions on K(x) and g(xu), we prove the existence of ground state solutions by variational methods.

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Acknowledgements

The authors wish to thank the anonymous referees very much for carefully reading this paper and suggesting many valuable comments. P. Chen was supported by the Research Foundation of Education Bureau of Hubei Province, China (Grant No. Q20192505). X. Liu was partially supported by the National Natural Science Foundation of China (Grant No. 11771342).

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Correspondence to Peng Chen.

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Chen, P., Liu, X. Ground states for asymptotically linear fractional Schrödinger–Poisson systems. J. Pseudo-Differ. Oper. Appl. 12, 8 (2021). https://doi.org/10.1007/s11868-021-00390-2

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Keywords

  • Fractional Schrödinger–Poisson system
  • Asymptotically linear
  • Variational methods

Mathematics Subject Classification

  • 35J50
  • 35R11