Ground state solutions for a critical quasilinear Choquard equation with periodic potential

In this paper, we study the following Choquard–type problem (Equation Presented) where N ≥ 3, 2 ≤ p < N, λ > 0 is a parameter, (N − 2p)+ < α < N and p∗α := (Formula Presented) is the Hardy–Littlewood–Sobolev critical exponent. The potential V ∈ C(RN , R) is assumed to be periodic, while Q ∈ C(RN , R) is bounded, and f is a C1–reaction term. Under suitable growth and monotonicity assumption on f, we establish the existence of ground state solution without assuming the Ambrosetti–Rabinowitz condition, provided that λ > 0 is sufficiently large. Our approach is variational, and relies on several key tools, including the Mountain Pass Theorem, the Nehari manifold method, the concentration–compactness principle, and the analysis of a suitable limiting problem.