Asymptotic profile of ground states for the Schrödinger–Poisson–Slater equation. (May 2022)

• Record Type: Journal Article
• Authors: Liu, Zeng; Moroz, Vitaly
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: 35J61 primary 35B09 35B33 35B40 35Q55 45K05; Schrödinger–Poisson–Slater equation -- Schrödinger–Maxwell equation -- Riesz potential -- Nonlocal semilinear elliptic problem -- Pohožaev identity -- Variational method -- Ground state; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112778
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the Schrödinger–Poisson–Slater equation − Δ u + u + λ ( I 2 ∗ | u | 2 ) u = | u | p − 2 u in R 3, where p ∈ ( 3, 6 ) and λ > 0 . By using direct variational analysis based on the comparison of the ground state energy levels, we obtain a characterization of the limit profile of the positive ground states for λ → ∞ .