Existence of Multispike Positive Solutions for a Nonlocal Problem in ℝ3

Jing Yang, Qiuxiang Bian and Na Zhao

Advances in Mathematical Physics, 2020, vol. 2020, issue 1

Abstract: In this paper, we study the following nonlinear Choquard equation −ϵ2Δu+Kxu=1/8πϵ2∫ℝ3u2y/x−ydyu,x∈ℝ3, where ϵ > 0 and K(x) is a positive bounded continuous potential on ℝ3. By applying the reduction method, we proved that for any positive integer k, the above equation has a positive solution with k spikes near the local maximum point of K(x) if ϵ > 0 is sufficiently small under some suitable conditions on K(x).

Date: 2020
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https://doi.org/10.1155/2020/7908978

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:7908978

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