Existence of nontrivial solutions for fractional Schrödinger‐Poisson system with sign‐changing potentials. (3rd May 2018)

• Record Type: Journal Article
• Authors: Che, Guofeng; Chen, Haibo; Shi, Hongxia; Wang, Zewei
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 13(2018)
• Page Start: 5050
• Page End: 5064
• Publication Date: 2018-05-03
• Subjects: fractional Schrödinger‐Poisson system -- nodal solution -- positive solution -- variational methods; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4951
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we consider the following fractional Schrödinger‐Poisson system ( − Δ ) α u + V ( x ) u + K ( x ) ϕ u = f ( x ) | u | q − 2 u, in R 3, ( − Δ ) t ϕ = K ( x ) u 2, in R 3, where 0 < t ≤ α < 1, q ∈ ( 4, 2 α ∗ ), and 4 α +2 t ≥3 and the functions V ( x ), K ( x ) and f ( x ) have finite limits as | x |→ ∞ . By imposing some suitable conditions on the decay rate of the functions, we prove that the above system has two nontrivial solutions. One of them is positive and the other one is sign‐changing. Recent results from the literature are generally improved and extended.