Normalized solutions for a biharmonic Choquard equation with exponential critical growth in ℝ⁴

2022/10/03 by Wenjing Chen, Chen, Wenjing, Zexi Wang +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.00887

openalex publication_date 2022/10/03 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the following biharmonic Choquard type equation \beginsplit \ γΔ²u-βΔu=λu+(I_μ*F(u))f(u), \quadin ℝ⁴, ∫_ℝ⁴|u|²dx=c² · gt;0, u∈ H²(ℝ⁴), . \endsplit where γ>0, β≥0, λ∈ ℝ, I_μ=(1)/(|x|^μ) with μ∈ (0,4), F(u) is the primitive function of f(u), and f is a continuous function with exponential critical growth. We can prove the existence of ground state normalized solutions for the above problem when the nonlinearity f satisfies some conditions.

Cited by

• Complete Spectrum and Sharp Local Stability for the Critical Exponential Biharmonic Choquard Equation in \(\mathbb R⁴\)

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