Existence of least energy solutions for a quasilinear Choquard equation

The present paper is devoted to the quasilinear Choquard equation driven by the p-Laplacian operator (Formula presented) where 2 ≤ p < N, Iα denotes the Riesz potential of order α ∈ (0, N), and G ∈ C1(R, R). Assuming Berestycki–Lions type conditions on G, we prove the existence of a least energy solution u ∈ W1,p(RN) by means of variational methods. Moreover, we establish some qualitative properties of u when G is even and non–decreasing.