Volume 48, Issue 12 pp. 12292-12308
RESEARCH ARTICLE

Semiclassical States for Fractional Choquard Equations With a Potential Well

Jie Yang

Jie Yang

School of Mathematics and Computational Science, Huaihua University, Huaihua, China

Key Laboratory of Intelligent Control Technology for Wuling-Mountain Ecological Agriculture, Huaihua, China

Contribution: ​Investigation, Writing - original draft, Writing - review & editing

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Haibo Chen

Corresponding Author

Haibo Chen

School of Mathematics and Statistics, Central South University, Changsha, China

Correspondence:

Haibo Chen ([email protected])

Contribution: Conceptualization, Writing - review & editing

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First published: 08 May 2025

Funding: J. Yang is supported by the Natural Science Foundation of Hunan Province of China (2023JJ30482 and 2022JJ30463), the Research Foundation of Education Bureau of Hunan Province (23A0558 and 22A0540), and the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province.

ABSTRACT

In this paper, we studied the existence and concentration behavior of positive solutions for a fractional Choquard equation involving a small parameter and a nonlocal nonlinearity. Under suitable assumptions on the potential function and the nonlinear term, we established two main results. First, for sufficiently small parameters, the equation admits multiple positive solutions, with the number of solutions depending on the topological structure of the potential's minimum set. Moreover, these solutions concentrate near this set as the parameter tends to zero. Second, we proved the existence of a single-peak solution whose peak converges to the potential's minimum set, and its rescaled version approaches a least energy solution of the associated limiting problem.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The authors have nothing to report.

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