Asymptotic Analysis of Multiple Solutions for Perturbed Choquard Equations

Tao Wang ()
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Tao Wang: Hunan University of Science and Technology

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 135-142

Abstract: 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.

Keywords: Choquard equation; convergence; Hartree type nonlocal term; perturbation; variational methods; 35B20; 35B40; 35J20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0389-5

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