In this study, we explore the existence of positive solutions for a category of asymptotically periodic generalized quasilinear elliptic equations in \({\mathbb {R}}^{N}\) exhibiting supercritical growth and discontinuous perturbation. The process involves reducing the generalized quasilinear equation to a semilinear one through a change of variable. Subsequently, we formulate an auxiliary problem associated with the semilinear equation. Utilizing the Mountain Pass Theorem for locally Lipschitz functional and the concentration compactness principle, we establish the existence of positive solutions to this auxiliary problem. Finally, we obtain a positive solution for the given problem through a truncation argument.
