Multiplicity of positive solutions for the fractional Schrödinger–Poisson system with critical nonlocal term

• Published in: Bulletin of mathematical sciences Vol. 14; no. 2
• Main Authors: Dou, Xilin, He, Xiaoming, Rădulescu, Vicenţiu D.
• Format: Journal Article
• Language: English
• Published: World Scientific Publishing Company 01.08.2024; World Scientific Publishing
• Subjects: critical nonlocal term; fractional Schrödinger–Poisson system; Ljusternik–Schnirelmann category; Positive solutions; variational method; critical nonlocal term; Positive solutions; fractional Schrödinger–Poisson system; variational method; Ljusternik–Schnirelmann category

This paper deals with the following fractional Schrödinger–Poisson system: ( − Δ ) s u + u − K ( x ) ϕ | u | 2 s ∗ − 3 u = f λ ( x ) | u | q − 2 u , x ∈ ℝ 3 , ( − Δ ) s ϕ = K ( x ) | u | 2 s ∗ − 1 , x ∈ ℝ 3 with multiple competing potentials and a critical nonlocal term, where s ∈ ( 0 , 1 ) , q ∈ (...