On equilibrium states for certain partially hyperbolic endomorphisms with one-dimensional center

In this paper, the equilibrium states for a non-degenerate $C^2$ partially hyperbolic endomorphism $f$ on a closed Riemannian manifold $M$ with one-dimensional center bundle are investigated. Applying the criterion of Climenhaga-Thompson (\cite{CT21}) and the method of Mongez-Pacifico (\cite{Mongez}), we use the techniques of inverse limit to obtain the uniqueness and robustness of equilibrium states for $f$ and any Hölder continuous potential satisfying certain conditions about the unstable pressure and stable pressure.