Normalized ground states for a biharmonic Choquard equation with exponential critical growth

2022/11/24 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 and Algebraic Topology #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2211.13701

openalex publication_date 2022/11/24 · openalex created_date 2022/11/30 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the normalized ground state solution for the following biharmonic Choquard type problem \beginsplit \ Δ²u-βΔu=λu+(I_μ*F(u))f(u), \quadin ℝ⁴, ∫_ℝ⁴|u|²dx=c², u∈ H²(ℝ⁴), . \endsplit where β≥0, c>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 in the sense of the Adams inequality. By using a minimax principle based on the homotopy stable family, we obtain that the above problem admits at least one ground state normalized solution.

Cited by

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

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