Abstract
In this paper, we study the following Choquard equations with small perturbation f
where N ≥ 3 and Iα denotes the Riesz potential. As is known that the above equation has a ground state uα and a bound state vα by fibering maps (see [22] or [23]), our aim is to show that for fixed \(p \in (1,\frac{N}{N-2})\), uα and vα converge to a ground state and a bound state of the limiting local problem respectively, as α → 0.
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The author thanks the editor and anonymous referees for their careful reading and helpful suggestions.
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Research was supported partially by the Scientific Research Fund of Hunan Provincial Education Department (19C0781, 19A179) and the Natural Science Foundation of Hunan Province (Grant No. 2018JJ3136)
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Wang, T. Asymptotic Analysis of Multiple Solutions for Perturbed Choquard Equations. Indian J Pure Appl Math 51, 135–142 (2020). https://doi.org/10.1007/s13226-020-0389-5
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DOI: https://doi.org/10.1007/s13226-020-0389-5