Multi-Peak solutions to Chern-Simons-Schrödinger systems with non-radial potential

2020/07/06 by Jin Deng, Deng, Jin, Long, Wei +2
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2007.02499

openalex publication_date 2020/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the existence of static solutions to the nonlinear Chern-Simons-Schrödinger system \-ihD₀Ψ-h²(D₁D₁+D₂D₂)Ψ+VΨ=|Ψ|^p-2Ψ,
∂₀A₁-∂₁A₀=-\frac 12ih[ΨD₂Ψ-ΨD₂Ψ],
∂₀A₂-∂₂A₀=\frac 12ih[ΨD₁Ψ-ΨD₁Ψ],
∂₁A₂-∂₂A₁=-\frac12|Ψ|², . where p>2 and non-radial potential V(x) satisfies some certain conditions. We show that for every positive integer k, there exists h₀>0 such that for 0

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