Nonlocal Pertubations of Fractional Choquard Equation

2017/05/16 by Gurpreet Singh, Singh, Gurpreet
Mathematics · #35A15 #35J60 #35Q40 #35R11 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1705.05775

openalex publication_date 2017/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the equation (-Δ)^su+V(x)u= (I_α*|u|^p)|u|^p-2u+λ(I_β*|u|^q)|u|^q-2u in \R^N, where I_γ(x)=|x|^-γ for any γ∈ (0,N), p, q >0, α,β∈ (0,N), N≥ 3 and λ∈ R. First, the existence of a groundstate solutions using minimization method on the associated Nehari manifold is obtained. Next, the existence of least energy sign-changing solutions is investigated by considering the Nehari nodal set.

Citations

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• On Gravity's role in Quantum State Reduction

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