Normalized solutions to the Chern-Simons-Schrödinger system: the supercritical case

2024/01/01 by Liejun Shen, Marco Squassina, Shen, Liejun +1
Computer Science · Mathematics · #35B06 #35J20 #35J61 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2401.00623

openalex publication_date 2024/01/01 · openalex created_date 2024/01/03 · openalex updated_date 2026/07/28

Abstract

We are concerned with the existence of normalized solutions for a class of generalized Chern-Simons-Schrödinger type problems with supercritical exponential growth -Δu +λu+A₀ u+∑_j=1²A_j² u=f(u), ∂₁A₂-∂₂A₁=-(1)/(2)|u|², ∂₁A₁+∂₂A₂=0, ∂₁A₀=A₂|u|², ∂₂A₀=-A₁|u|², ∫_ℝ²|u|²dx=a², where a≠0, λ∈ ℝ is known as the Lagrange multiplier and f∈ C¹(ℝ) denotes the nonlinearity that fulfills the supercritical exponential growth in the Trudinger-Moser sense at infinity. Under suitable assumptions, combining the constrained minimization approach together with the homotopy stable family and elliptic regularity theory, we obtain that the problem has at least a ground state solution.

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