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This paper deals with the quasilinear parabolic-elliptic Keller-Segel systemwith logistic source, \begin{align*}  u_t=\Delta (u+1)^m - \chi \nabla \cdot (u(u+1)^{\alpha - 1} \nabla v)  + \lambda(|x|) u - \mu(|x|) u^\kappa,  \quad  0=\Delta v - v + u,  \quad x\in\Omega,\ t>0,  \end{align*} where $\Omega:=B_{R}(0)\subset\mathbb{R}^n\ (n\ge3)$ is a ballwith some $R>0$; $m>0$, $\chi>0$, $\alpha>0$ and $\kappa\ge1$; $\lambda$ and$\mu$ are spatially radial nonnegative functions. About this problem, Winkler(Z. Angew. Math. Phys.; 2018; 69; Art. 69, 40) found the condition for $\kappa$such that solutions blow up in finite time when $m=\alpha=1$. In the case that$m=1$ and $\alpha\in(0,1)$ as well as $\lambda$ and $\mu$ are constant, someconditions for $\alpha$ and $\kappa$ such that blow-up occurs were obtained ina previous paper (Math. Methods Appl. Sci.; 2020; 43; 7372-7396). Moreover, inthe case that $m\ge1$ and $\alpha=1$ Black, Fuest and Lankeit(arXiv:2005.12089[math.AP]) showed that there exists initial data such thatsolutions blow up in finite time under some conditions for $m$ and $\kappa$.The purpose of the present paper is to give conditions for $m\ge1$, $\alpha>0$and $\kappa\ge1$ such that solutions blow up in finite time.

Blow-up in a quasilinear parabolic-elliptic Keller-Segel system with logistic source