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.