This paper deals with a class of attraction-repulsion chemotaxis systems in a smoothly bounded domain. When the system is parabolic-elliptic-parabolic-elliptic and the domain is $ n $-dimensional, if the repulsion effect is strong enough then the solutions of the system are globally bounded. Meanwhile, when the system is fully parabolic and the domain is either one-dimensional or two-dimensional, the system also possesses a globally bounded classical solution.
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