A note on the boundedness in a chemotaxis-growth system with nonlinear sensitivity

摘要

This paper deals with a parabolic-elliptic chemotaxis-growth system withnonlinear sensitivityunder homogeneous Neumann boundary conditions in a smooth bounded domain W ?Rn (n ≥ 1), where c > 0, the chemotactic sensitivity y(u) ≤ (u + 1)q with q > 0,g(u) ≤ (u + 1)l with l 2 R and f(u) is a logistic source. The main goal of this paper isto extend a previous result on global boundedness by Zheng et al. [J. Math. Anal. Appl.424(2015), 509–522] under the condition that 1 ≤ q + l < n2 + 1 to the case q + l < 1.