We consider the parabolic–elliptic chemotaxis-growth system
under no-flux boundary conditions in a smoothly bounded domain , N≥1, where χ,μ,m,α and γ are prescribed positive parameters fulfilling m≥1 and γ≥1.
Recently, it has been proved in Galakhov et al. (2016) that if either α>m+γ−1 or α=m+γ−1 and , for any given this system possesses a global and bounded classical solution. The present work further shows that the same conclusion still holds for the critical case α=m+γ−1 and .