Locations of spikes for linearly coupled Schrödinger systems. (21st September 2021)

• Record Type: Journal Article
• Authors: Jin, Ke; Shen, Zifei; Wang, Lushun
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 18(2022)
• Page Start: 14915
• Page End: 14936
• Publication Date: 2021-09-21
• Subjects: ground states -- linearly coupled terms -- Schrödinger system -- spikes; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7752
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we consider the following Schrödinger system with linearly coupled terms: − ε 2 Δ u + u = | u | 2 u + λ v in Ω, ( A 1 ) − ε 2 Δ v + v = | v | 2 v + λ u in Ω, where ε > 0, 0 < λ < 1, and Ω is a bounded smooth domain in ℝ 3 . Under the Dirichlet or Neumann boundary conditions, we study the locations and interaction of spikes for ground states of (A1 ) by the variation method, maximum principle, and blow up technique.