Abstract
Abstract We are interested in the existence of a ground state solution for the fractional Schrodinger-Poisson system with critical growth { ( − Δ ) s u + ϕ u = g ( u ) + | u | 2 s * − 2 u , in R 3 , ( − Δ ) t ϕ = u 2 , in R 3 , where 2 s * = 6 3 − 2 s , s , t ∈ ( 0 , 1 ) and 2 s + 2 t > 3 . Under some mild assumptions on g ( u ) , using the compactness lemma of Strauss, a positive ground state solution is obtained by approximating the Pohozaev-Nehari type ground state solutions of the subcritical problems.
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