Existence and asymptotic behavior of least energy sign-changing solutions for Schrodinger-Poisson systems with doubly critical exponents

2022/11/28 by Xiaoping Chen, Chun‐Lei Tang, Chen, Xiao-Ping +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2211.15316

openalex publication_date 2022/11/28 · openalex created_date 2022/12/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the following Schrödinger-Poisson system with critical nonlinearity and critical nonlocal term due to the Hardy-Littlewood-Sobolev inequality \begincases -Δu+u+λϕ|u|³u =|u|⁴u+ |u|^q-2u, amp; x ∈ ℝ³,
-Δϕ=|u|⁵, amp; x ∈ ℝ³, \endcases where λ∈ ℝ is a parameter and q∈(2,6). If λ≥ ((q+2)/(8))² and q∈(2,6), the above system has no nontrivial solution. If λ∈ (λ^*,0) for some λ^*<0, we obtain a least energy radial sign-changing solution u_λ to the above system. Furthermore, we consider λ as a parameter and analyze the asymptotic behavior of u_λ as λ→ 0^-.

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