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Teng, Kaimin
Journal of Differential Equations, 09/2016, Letnik: 261, Številka: 6Journal Article
In this paper, we study the existence of ground state solutions for the nonlinear fractional Schrödinger–Poisson system with critical Sobolev exponent{(−Δ)su+V(x)u+ϕu=μ|u|q−1u+|u|2s⁎−2u,in R3,(−Δ)tϕ=u2,in R3, where μ∈R+ is a parameter, 1<q<2s⁎−1=3+2s3−2s, s,t∈(0,1) and 2s+2t>3. Under certain assumptions on V(x), using the method of Pohozaev–Nehari manifold and the arguments of Brezis–Nirenberg, the monotonic trick and global compactness Lemma, we prove the existence of a nontrivial ground state solution.
