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Asymptotic Analysis of Multiple Solutions for Perturbed Choquard Equations

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Abstract

In this paper, we study the following Choquard equations with small perturbation f

$$-\Delta u + V(x)u = (I_\alpha * |u|^p)|u|^{p-2}u+f(x), x\in \mathbb{R}^N.$$

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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Acknowledgement

The author thanks the editor and anonymous referees for their careful reading and helpful suggestions.

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Authors and Affiliations

  1. College of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, Hunan, 411201, P. R. China

    Tao Wang

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  1. Tao Wang
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Correspondence to Tao Wang.

Additional information

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

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