Least energy solutions to a class of nonlocal Schrödinger equations

Yong-Chao Zhang; Yong-Chao Zhang

doi:10.3934/math.20241009

AIMS Mathematics

2024, Volume 9, Issue 8: 20763-20772. doi: 10.3934/math.20241009

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Least energy solutions to a class of nonlocal Schrödinger equations

Yong-Chao Zhang ^,

School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Taishan Road 143, Qinhuangdao 066004, China

Received: 10 May 2024 Revised: 18 June 2024 Accepted: 20 June 2024 Published: 26 June 2024
MSC : 35Q55, 35J60, 35A15

We explore a class of nonlocal Schrödinger equations that include not only fractional Schrödinger equations but also other nonlocal Schrödinger equations studied in the literature. We prove the existence of least energy solutions to this class of equations by the variational method, which extends the results obtained by Gu et al. (2018) and Xiang et al. (2019).
- least energy solution,
- nonlocal Schrödinger equation,
- critical point,
- Nehari manifold
Citation: Yong-Chao Zhang. Least energy solutions to a class of nonlocal Schrödinger equations[J]. AIMS Mathematics, 2024, 9(8): 20763-20772. doi: 10.3934/math.20241009

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Abstract

We explore a class of nonlocal Schrödinger equations that include not only fractional Schrödinger equations but also other nonlocal Schrödinger equations studied in the literature. We prove the existence of least energy solutions to this class of equations by the variational method, which extends the results obtained by Gu et al. (2018) and Xiang et al. (2019).

References

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