Uniform-in-time boundedness in a class of local and nonlocal nonlinear attraction-repulsion chemotaxis models with logistics

This article deals with a class of chemotaxis systems describing mechanisms from mathematical biology. In the specific, for a rather general class of attraction-repulsion models, with nonlinear productions, diffusion, sensitivities and logistic term, we are interested in deriving interplays on the parameters involved in the problem capable to ensure globality and boundedness of related solutions. This project is precisely contextualized in the frame of a series of results dealing with local and nonlocal, and linear and nonlinear, attraction-repulsion chemotaxis systems. For these problems, rooms of improvements are still open; in this sense, this research exactly enhances and extends already known analyses in the literature. More specifically, a direct comparison with [Jiao, Jadlovsk\'a, Li, Nonlinear Anal. Real World Appl., 2023; Ren, Liu, Math. Models Methods Appl. Sci., 2020; Chiyo, Yokota, Z. Angew. Math. Phys., 2022; Columbu, Frassu, Viglialoro, Appl. Anal., 2023] is carried out.