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Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ 3
Author(s) -
Yin Rong,
Zhang Jihui,
Shang Xudong
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6541
Subject(s) - mathematics , ground state , term (time) , schrödinger's cat , poisson distribution , state (computer science) , variational method , mathematical physics , mathematical analysis , quantum mechanics , physics , statistics , algorithm
This paper is dedicated to studying the following Schrödinger–Poisson system− Δ u + V ( x ) u − K ( x ) ϕ | u | 3 u = a ( x ) f ( u ) ,x ∈ ℝ 3 ,− Δ ϕ = K ( x ) | u | 5 ,x ∈ ℝ 3 .Under some different assumptions on functions V ( x ), K ( x ), a ( x ) and f ( u ), by using the variational approach, we establish the existence of positive ground state solutions.