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Remarks on the Berestycki–Lions Conditions for the Existence of Solutions

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Abstract

In this paper, we are concerned with the following Schrödinger equation

$$ - \Delta u = g(u),\,\,\,\,\,\,x \in {\mathbb{R}^N}.$$

We give a new approach and a brief proof to show the existence of infinitely many solutions and ground state solutions with g satisfying the Berestycki–Lions conditions [Arch. Rational Mech. Anal., 1983, 82(4): 313–345, 347–357].

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References

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Acknowledgements

This work is supported by National Natural Science Foundation of China (No. 12371120), the China Postdoctoral Science Foundation (No. 2020M683251), and the special subsidy from Chongqing Human Resources and Social Security Bureau.

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Author notes

  1. Xiaoqi Liu

    Present address: School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, China

Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Xiaoqi Liu, Jincai Kang & Chunlei Tang

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  1. Xiaoqi Liu
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  2. Jincai Kang
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  3. Chunlei Tang
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Correspondence to Chunlei Tang.

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Conflict of Interest The authors declare no conflict of interest.

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Liu, X., Kang, J. & Tang, C. Remarks on the Berestycki–Lions Conditions for the Existence of Solutions. Front. Math (2024). https://doi.org/10.1007/s11464-022-0097-z

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  • DOI: https://doi.org/10.1007/s11464-022-0097-z

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