Premium
Existence and concentration of solutions for Schrödinger–Poisson system with steep potential well
Author(s) -
Zhang Wen,
Tang Xianhua,
Zhang Jian
Publication year - 2016
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.3712
Subject(s) - mathematics , bounded function , poisson distribution , schrödinger's cat , nonlinear system , set (abstract data type) , mathematical physics , mathematical analysis , quantum mechanics , physics , statistics , computer science , programming language
This paper is concerned with the nonlinear Schrödinger–Poisson system− Δ u + λV ( x ) u + K ( x ) ϕu = f ( x , u ) ,x ∈R 3 ,− Δ ϕ = K ( x ) u 2 ,x ∈R 3 ,where λ > 0 is a parameter. We require that V ≥0 and has a bounded potential well V −1 (0). Combining this with other suitable assumptions on K and f , the existence of nontrivial solutions is obtained by using variational methods. Moreover, the concentration of solutions is also explored on the set V −1 (0) as λ → ∞ . Copyright © 2015 John Wiley & Sons, Ltd.