EXISTENCE OF GROUND STATE SOLUTIONS FOR A CHOQUARD DOUBLE PHASE PROBLEM

In this paper we study quasilinear elliptic equations driven by the double phase operator involving a Choquard term of the form −Lp,q(u) + |u|p−2u+ a(x)|u|q−2u = (∫ RN F (y, u) |x− y|μ dy ) f(x, u) in R , where Lp,q is the double phase operator given by Lp,q(u) := div ( |∇u|p−2∇u+ a(x)|∇u|q−2∇u ) , u ∈ W 1,H(RN ), 0 < μ < N , 1 < p < N , p < q < p + αp N , 0 ≤ a(·) ∈ C0,α(RN ) with α ∈ (0, 1] and f : RN × R → R is a continuous function that satisfies a subcritical growth. Based on the Hardy-Littlewood-Sobolev inequality, the Nehari manifold and variational tools, we prove the existence of ground state solutions of such problems under different assumptions on the data.