In this paper, we study an attraction-repulsion Keller-Segel chemotaxis model with logistic source
in a smooth bounded domain
$f(u)≤ a-bu^θ, \ \ u≥ 0,\ \ \mathrm{with~some} \ \ a≥ 0,b>0,θ≥1.$
When
$\begin{cases} θ > \max\{1,3-\frac6n\}, &\text{when }\ \ 1≤ n≤ 5,\\ θ≥ 2, &\text{when }\ \ 6≤ n≤ 9,\\ θ>1+\frac{2(n-4)}{n+2}, &\text{when} \ \ \ n≥10.\\\end{cases}$
Furthermore, when
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