The following chemotaxis-consumption problem with no-flux boundary conditions has been considered \( \left \{ \textstyle\begin{array}{l@{\quad }l} v_{t}=\Delta (\omega ^{-\alpha }v)+\eta v^{\beta }(1-\int _{\Omega }v^{ \kappa }), & (x,t) \in \Omega \times (0,T_{\max }), \\ \omega _{t}=\Delta \omega -v^{\gamma }\omega , & (x,t) \in \Omega \times (0,T_{\max }), \end{array}\displaystyle \right . \) within a smoothly bounded domain $\Omega \subset \mathbb{R}^{n}(n\geq 3)$ , where the parameters $\kappa >\beta >1$ , $\alpha , \gamma ,\eta >0$ , and $T_{\max }\in (0,\infty ]$ . This paper mainly examines the effects of nonlinear dissipation and nonlocal logistic feedback on solutions. Specifically, for all suitably regular initial data, it has been established that if \( 2\leq \beta < 1+\frac{2\kappa }{n} \ \text{and} \ \beta +\kappa >\gamma (n+2), \) or \( 1< \beta < 2 \ \text{and} \ \beta +\kappa > \max \{\frac{n+4}{2}, \gamma (n+2)\}, \) then the above system has a global classical solution. Compared with previous research results, the novelty (or difficulty) of this paper lies in the combination of non-local terms and nonlinear dissipation.
