This paper concerns the existence of bounded classical solutions to the attraction-repulsion chemotaxis system with logistic source(⋆)$\{\begin{array}{c}{u}_t=\mathrm{\Delta }u-\chi \mathrm{\nabla }\cdot (u\mathrm{\nabla }v)+\xi \mathrm{\nabla }\cdot (u\mathrm{\nabla }w)+f(u),x\in \mathrm{\Omega },t>0,\hfill \\ 0=\mathrm{\Delta }v-\beta v+\alpha u,x\in \mathrm{\Omega },t>0\hfill \\ 0=\mathrm{\Delta }w-\delta w+\gamma u,x\in \mathrm{\Omega },t>0\hfill \end{array}$ in a smooth bounded domain $\mathrm{\Omega }\subseteq {\mathbb{R}}^N(N\ge 1)$, subject to nonnegative initial data and homogeneous Neumann boundary conditions, where $f(u)\le a-b{u}^r$ for all $u\ge 0$ with some $a\ge 0,b>0$ and $r\ge 1$. Here $\chi ,\alpha ,\xi ,\beta$ as well as γ and δ are positive constants. It is proved that the corresponding system $(\star )$ possesses a unique global bounded classical solution in the balance case $\chi \alpha =\xi \gamma$ with $r>\frac{2N-2}{N}$ or, the attraction domination case $\xi \alpha >\xi \gamma$ with $b\ge \frac{{(N-2)}_{+}}{N}(\chi \alpha -\xi \gamma )$ and $r=2$, respectively. The study of this paper improves the results in Li-Xiang (2016) [12], Xu-Zheng (2018) [39], Wang (2016) [26] as well as Zhao et al. (2017) [42] and Tello-Winkler (2007) [23], in which, the assumption $b>\frac{{(N-2)}_{+}}{N}(\chi \alpha -\xi \gamma )$ (see Li-Xiang (2016) as well as Wang (2016) and Zhao et al. (2017)) or $b>\frac{{(N-2)}_{+}}{N}\chi$ (see Tello-Winkler (2007)) or $r>\frac{2N+2}{N+2}$ (see Xu-Zheng (2018)) or $r>\frac{\sqrt{N^2+4N}-N}{2}$ (see Li-Xiang (2016)) are intrinsically required.

本文涉及具有逻辑源(⋆)的吸引-排斥趋化系统的有界经典解的存在性$\{\begin{array}{c}{你}_{吨}=\mathrm{\Delta }你-\chi \mathrm{\nabla }\cdot (你\mathrm{\nabla }v)+\xi \mathrm{\nabla }\cdot (你\mathrm{\nabla }瓦)+F(你),X\in \mathrm{\Omega },吨>0,\hfill \\ 0=\mathrm{\Delta }v-\beta v+\alpha 你,X\in \mathrm{\Omega },吨>0\hfill \\ 0=\mathrm{\Delta }瓦-\delta 瓦+\gamma 你,X\in \mathrm{\Omega },吨>0\hfill \end{array}$ 在光滑有界域中 $\mathrm{\Omega }\subseteq {\mathbb{电阻}}^N(N\ge 1)$，受非负初始数据和齐次 Neumann 边界条件的约束，其中 $F(你)\le \mathrm{一种}-乙{你}^r$ 对所有人 $你\ge 0$ 和一些 $\mathrm{一种}\ge 0,乙>0$ 和 $r\ge 1$. 这里$\chi ,\alpha ,\xi ,\beta$以及γ和δ是正常数。证明相应的系统$(\star )$ 在平衡情况下具有唯一的全局有界经典解 $\chi \alpha =\xi \gamma$ 和 $r>\frac{2N-2}{N}$ 或者，吸引力支配案例 $\xi \alpha >\xi \gamma$ 和 $乙\ge \frac{{(N-2)}_{+}}{N}(\chi \alpha -\xi \gamma )$ 和 $r=2$， 分别。本文的研究改进了 Li-Xiang (2016) [12]、Xu-Zeng (2018) [39]、Wang (2016) [26] 以及 Zhao 等人的结果。(2017) [42] 和 Tello-Winkler (2007) [23]，其中，假设$乙>\frac{{(N-2)}_{+}}{N}(\chi \alpha -\xi \gamma )$ （参见 Li-Xiang (2016) 以及 Wang (2016) 和 Zhao et al. (2017)）或 $乙>\frac{{(N-2)}_{+}}{N}\chi$ （参见 Tello-Winkler (2007)）或 $r>\frac{2N+2}{N+2}$ （见徐正（2018））或 $r>\frac{\sqrt{N^2+4N}-N}{2}$ （见 Li-Xiang (2016)）本质上是必需的。