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Asymptotic Analysis of Multiple Solutions for Perturbed Choquard Equations

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  • Tao Wang

    (Hunan University of Science and Technology)

Abstract

In this paper, we study the following Choquard equations with small perturbation f$$-\Delta u + V(x)u = (I_\alpha * |u|^p)|u|^{p-2}u+f(x), x\in \mathbb{R}^N.$$−Δu+V(x)u=(Iα*|u|p)|u|p−2u+f(x),x∈RN. 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 $$p \in (1,\frac{N}{N-2})$$p∈(1,NN−2), uα and vα converge to a ground state and a bound state of the limiting local problem respectively, as α → 0.

Suggested Citation

  • Tao Wang, 2020. "Asymptotic Analysis of Multiple Solutions for Perturbed Choquard Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 135-142, March.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:1:d:10.1007_s13226-020-0389-5
    DOI: 10.1007/s13226-020-0389-5
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    References listed on IDEAS

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    1. Tao Xie & Lu Xiao & Jun Wang, 2015. "Existence of Multiple Positive Solutions for Choquard Equation with Perturbation," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-10, September.
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