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Existence of Multispike Positive Solutions for a Nonlocal Problem in ℝ3

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  • Jing Yang
  • Qiuxiang Bian
  • Na Zhao

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).

Suggested Citation

  • Jing Yang & Qiuxiang Bian & Na Zhao, 2020. "Existence of Multispike Positive Solutions for a Nonlocal Problem in ℝ3," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:7908978
    DOI: 10.1155/2020/7908978
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