  This paper is framed in a series of studies on attraction-repulsion
chemotaxis models combining different effects: nonlinear diffusion and
sensitivities and logistic sources, for the dynamics of the cell density, and
consumption and/or production impacts, for those of the chemicals. In
particular, herein we focus on the situation where the signal responsible of
gathering tendencies for the particles' distribution is produced, while the
opposite counterpart is consumed. In such a sense, this research complements
two recent results, where the chemicals evolve according to different laws.
