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

摘要

In this paper, we consider the following Schrödinger–Poisson systemwhere q ∈ (3, 6) and λ, μ > 0 are positive parameters. Since 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 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 → ∞.