Wang, Xiaoli; Rong, Yuetang; Dong, Miaona; He, Di The global bifurcation for a prey-predator model with cross-diffusion and B-D functional response. (Chinese. English summary) Zbl 1374.35053 Basic Sci. J. Text. Univ. 29, No. 3, 319-325 (2016). Summary: This paper concerns the existence of positive solutions for a predator-prey model with cross-diffusion and B-D functional response under homogeneous Dirichlet boundary conditions. By the maximum principle, a priori estimate of positive solutions is obtained. By considering the related eigenvalue problems, two unbounded neutral curves are given. Then by Crandall-Rabinowitz bifurcation theory, the existence of positive solutions to a local bifurcation is proved. Finally, the local bifurcation is developed to the global one. MSC: 35B32 Bifurcations in context of PDEs 35B09 Positive solutions to PDEs 35B45 A priori estimates in context of PDEs 92D25 Population dynamics (general) Keywords:cross-diffusion; predator-prey model; apriori estimate; global bifurcation PDFBibTeX XMLCite \textit{X. Wang} et al., Basic Sci. J. Text. Univ. 29, No. 3, 319--325 (2016; Zbl 1374.35053) Full Text: DOI