Ground state solution for strongly indefinite Choquard system. (July 2022)

• Record Type: Journal Article
• Authors: Chen, Jianqing; Zhang, Qian
• Is Part Of: Nonlinear analysis. Volume 220(2022)
• Publication Date: 2022-07
• Subjects: 35J05 -- 35J20 -- 35J60; Strongly indefinite functional -- Choquard system -- Periodic potential -- Ground state solution -- Generalized Nehari manifold; 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.2022.112855
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the following Choquard system in R N − Δ u + V ( x ) u = 2 q p + q ( I α ∗ | u | p ) | v | q − 2 v, − Δ v + V ( x ) v = 2 p p + q ( I α ∗ | v | q ) | u | p − 2 u, u ( x ) → 0 a n d v ( x ) → 0 a s | x | → ∞, where α ∈ ( 0, N ) and N + α N < p, q < 2 ∗ α, in which 2 ∗ α denotes N + α N − 2 if N ≥ 3 and 2 ∗ α ≔ ∞ if N = 1, 2 . I α is a Riesz potential. V is continuous, 1-periodic in x and 0 belongs to a spectral gap of − Δ + V . This system is subcritical in the sense of the Hardy–Littlewood–Sobolev inequality. Based on the generalized Nehari manifold, we obtain the existence of ground state solutions. Our results can be looked on as a generalization to results by Szulkin and Weth (2009).