Abstract
In this paper, we study the following nonlocal problem in \(\mathbb R^3\)
where \(\lambda >0\) is a real parameter and \(\mu >0\) is small enough. Under some suitable assumptions on V(x) and f(x, u), we prove the existence of ground state solutions for the problem when \(\lambda \) is large enough via variational methods. In addition, the concentration behavior of these ground state solutions is also investigated as \(\lambda \rightarrow +\infty \).
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Funding
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11661053, 11771198, 11901276 and 11961045), the Provincial Natural Science Foundation of Jiangxi, China (Grant Nos. 20181BAB201003, 20202BAB201001 and 20202BAB211004) and the Nanchang University Jiangxi Provincial Fiscal Science and Technology Special “Complete Rationing System” Pilot Demonstration Project (Grant No. ZBG20230418001).
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J. W. Huang wrote this paper, C. F. Chen provided the funding and the revision of the paper, and C. G. Yuan helped with some of the calculation and funding.
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Huang, J., Chen, C. & Yuan, C. Existence and Concentration of Ground State Solutions for a Schrödinger–Poisson-Type System with Steep Potential Well. Qual. Theory Dyn. Syst. 23, 59 (2024). https://doi.org/10.1007/s12346-023-00920-x
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DOI: https://doi.org/10.1007/s12346-023-00920-x