Existence and concentration of positive ground state solutions for nonlinear fractional Schrödinger‐Poisson system with critical growth

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In this paper, we study the following fractional Schrödinger‐Poisson system involving competing potential functions urn:x-wiley:mma:media:mma5289:mma5289-math-0001 where ϵ > 0 is a small parameter, f is a function of C1 class, superlinear and subcritical nonlinearity, , , t ∈ (0,1), V(x), K(x), and Q(x) are positive continuous functions. Under some suitable assumptions on V, K, and Q, we prove that there is a family of positive ground state solutions with polynomial growth for sufficiently small ϵ > 0, of which it is concentrating on the set of minimal points of V(x) and the sets of maximal points of K(x) and Q(x).