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

In this paper, we study the following Choquard–type problem [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] is a parameter, [Formula: see text] and [Formula: see text] is the Hardy–Littlewood–Sobolev critical exponent. The potential [Formula: see text] is assumed to be periodic, while [Formula: see text] is bounded, and [Formula: see text] is a [Formula: see text]–reaction term. Under suitable growth and monotonicity assumption on [Formula: see text], we establish the existence of ground state solution without assuming the Ambrosetti–Rabinowitz condition, provided that [Formula: see text] 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.