Lian, Tong; Yang, Wenbin; Li, Yanling Qualitative analysis of a predator-prey system with Smith growth for prey. (Chinese. English summary) Zbl 1449.35266 J. Biomath. 34, No. 2, 312-322 (2019). Summary: A Holling type-III predator-prey model with Smith growth subject to the homogeneous Neumann boundary condition is investigated in this paper. Firstly, the local stability of positive constant steady state solution is discussed. Secondly, we give a priori estimate of positive solutions. Finally, some sufficient conditions for the nonexistence and existence of nonconstant positive steady state solutions are derived. MSC: 35K57 Reaction-diffusion equations 35B09 Positive solutions to PDEs 35B35 Stability in context of PDEs Keywords:predator-prey model; Holling type-III functional response; Smith growth; positive steady state solution PDF BibTeX XML Cite \textit{T. Lian} et al., J. Biomath. 34, No. 2, 312--322 (2019; Zbl 1449.35266)