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This paper deals with the quasilinear attraction-repulsion chemotaxis system\begin{align*}  \begin{cases}  u_t=\nabla\cdot \big((u+1)^{m-1}\nabla u  -\chi u(u+1)^{p-2}\nabla v  +\xi u(u+1)^{q-2}\nabla w\big),\\[]  0=\Delta v+\alpha u-\beta v,\\[]  0=\Delta w+\gamma u-\delta w  \end{cases} \end{align*} in a bounded domain $\Omega \subset \mathbb{R}^n$$(n \in \mathbb{N})$ with smooth boundary $\partial \Omega$, where $m, p, q \in\mathbb{R}$, $\chi, \xi, \alpha, \beta, \gamma, \delta>0$ are constants. In thecase that $m=1$ and $p=q=2$, when $\chi\alpha-\xi\gamma<0$ and $\beta=\delta$,Tao-Wang (Math. Models Methods Appl. Sci.; 2013; 23; 1-36) proved that globalbounded classical solutions toward the spatially constant equilibrium$(\overline{u_0}, \frac{\alpha}{\beta}\overline{u_0},\frac{\gamma}{\delta}\overline{u_0})$ via the reduction to the Keller-Segelsystem by using the transformation $z:=\chi v-\xi w$, where $\overline{u_0}$ isthe spatial average of the initial data $u_0$. However, since the above systeminvolves nonlinearities, the method is no longer valid. The purpose of thispaper is to establish that global bounded classical solutions converge to thespatially constant equilibrium $(\overline{u_0},\frac{\alpha}{\beta}\overline{u_0}, \frac{\gamma}{\delta}\overline{u_0})$.

Stabilization for small mass in a quasilinear  parabolic--elliptic--elliptic attraction-repulsion chemotaxis system with  density-dependent sensitivity: repulsion-dominant case