2023/06/05 by Wenjing Chen, Chen, Wenjing, Zexi Wang +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2306.02963
openalex publication_date 2023/06/05 · openalex created_date 2023/06/07 · openalex updated_date 2026/07/28
In this paper, we study the existence of normalized ground state solutions for the following biharmonic Choquard system \beginsplit \ Δ2u=λ1 u+(Iμ*F(u,v))Fu (u,v), \quadin ℝ4, Δ2v=λ2 v+(Iμ*F(u,v)) Fv(u,v), \quadin ℝ4, ∫ℝ4|u|2dx=a2, ∫ℝ4|v|2dx=b2, u,v∈ H2(ℝ4), . \endsplit where a,b>0 are prescribed, λ1,λ2∈ ℝ, Iμ=(1)/(|x|μ) with μ∈ (0,4), Fu,Fv are partial derivatives of F and Fu,Fv have exponential subcritical or critical growth in the sense of the Adams inequality. By using a minimax principle and analyzing the behavior of the ground state energy with respect to the prescribed mass, we obtain the existence of ground state solutions for the above problem.