Normalized ground state solutions for the Chern–Simons–Schrödinger equations with mixed Choquard-type nonlinearities

Yipeng Qiu; Yingying Xiao; Yan Zhao; Shengyue Xu; Yipeng Qiu; Yingying Xiao; Yan Zhao; Shengyue Xu

doi:10.3934/math.20241677

AIMS Mathematics

2024, Volume 9, Issue 12: 35293-35307. doi: 10.3934/math.20241677

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Research article

Normalized ground state solutions for the Chern–Simons–Schrödinger equations with mixed Choquard-type nonlinearities

School of Mathematical Science, Jiangxi Science and Technology Normal University, 330038 Nanchang, Jiangxi, China

Received: 19 October 2024 Revised: 02 December 2024 Accepted: 10 December 2024 Published: 18 December 2024
MSC : 35J20, 35J60

In this paper, we study the existence and the limit behavior of normalized solutions for the Chern–Simons–Schrödinger equations with mixed Choquard-type nonlinearities and $ \frac{\alpha }{2}+2 < q < p < +\infty $. Moreover, we also get the relationship between the minimizer and the ground state solution under the Pohožaev–Nehari manifold of the Chern–Simons–Schrödinger equations.
- normalized solution,
- Chern–Simons–Schrödinger equations,
- Choquard-type nonlinearities,
- variational method
Citation: Yipeng Qiu, Yingying Xiao, Yan Zhao, Shengyue Xu. Normalized ground state solutions for the Chern–Simons–Schrödinger equations with mixed Choquard-type nonlinearities[J]. AIMS Mathematics, 2024, 9(12): 35293-35307. doi: 10.3934/math.20241677

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Abstract

In this paper, we study the existence and the limit behavior of normalized solutions for the Chern–Simons–Schrödinger equations with mixed Choquard-type nonlinearities and $ \frac{\alpha }{2}+2 < q < p < +\infty $. Moreover, we also get the relationship between the minimizer and the ground state solution under the Pohožaev–Nehari manifold of the Chern–Simons–Schrödinger equations.

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