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This paper deals with the fully parabolic attraction-repulsion chemotaxissystem with signal-dependent sensitivities, \begin{align*} \begin{cases}  u_t=\Delta u-\nabla \cdot (u\chi(v)\nabla v)  +\nabla \cdot (u\xi(w)\nabla w),  &x \in \Omega,\ t>0,\\[1.05mm]  v_t=\Delta v-v+u,  &x \in \Omega,\ t>0,\\[1.05mm]  w_t=\Delta w-w+u,  &x \in \Omega,\ t>0 \end{cases} \end{align*} under homogeneous Neumannboundary conditions and initial conditions, where $\Omega \subset \mathbb{R}^n$$(n \ge 2)$ is a bounded domain with smooth boundary, $\chi, \xi$ are functionssatisfying some conditions. Global existence and boundedness of classicalsolutions to the system with logistic source have already been obtained bytaking advantage of the effect of logistic dampening (J. Math. Anal. Appl.;2020;489;124153). This paper establishes existence of global bounded classicalsolutions despite the loss of logistic dampening.

Global existence and boundedness in a fully parabolic  attraction-repulsion chemotaxis system with signal-dependent sensitivities  without logistic source