Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case

2024/03/26 by Liejun Shen, Marco Squassina, Shen, Liejun +1
Mathematics · Physics and Astronomy · #35B06 #35J20 #58E50 #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.18014

openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schrödinger systems \ -Δu +A₀ u+∑_j=1²A_j² u=f(u)-a(x)|u|^p-2u, \newline ∂₁A₂-∂₂A₁=-(1)/(2)|u|²,~∂₁A₁+∂₂A₂=0, \newline ∂₁A₀=A₂|u|²,~ ∂₂A₀=-A₁|u|², . where a:\mathbb R²→\mathbb R⁺ is an external potential, p∈(1,2) and f∈ C(\mathbb R) denotes a nonlinearity that fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. By introducing an improvement of the version of Trudinger-Moser inequality, we are able to investigate the existence of positive ground state solutions for the given system using variational method.

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