Existence and concentration of ground state solutions for critical Schrödinger–Poisson system with steep potential well

Li-Feng Yin, Xing-Ping Wu and Chun-Lei Tang

Applied Mathematics and Computation, 2020, vol. 374, issue C

Abstract: In this paper, we consider the following Schrödinger–Poisson system{−Δu+(1+μg(x))u+ϕu=|u|4u+λ|u|q−2u,inR3,−Δϕ=u2,inR3,where q ∈ (3, 6) and λ, μ > 0 are positive parameters. Since f(u):=|u|4u+λ|u|q−2u with q ∈ (3, 4] does not satisfy the (AR) condition. Thus, we construct Nehari-Pohožaev-Palais-Smale sequence to overcome the boundedness of sequence. As q ∈ (4, 6), the boundedness of sequence is easily obtained. We need (g1) and (g2) to prove that cμ<13S32 independent of μ. Furthermore, we utilize the definition of the set of solutions to seek a ground state solution. Besides, the concentration behavior of the ground state solution is also described as μ → ∞.

Keywords: Schrödinger–Poisson system; Critical growth; Ground states; Pohožaev identity (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:374:y:2020:i:c:s0096300320300047

DOI: 10.1016/j.amc.2020.125035

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