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

Source abstract

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 C 1 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 ).