Positive Solutions for a Stationary Prey-Predator Model with Density-Dependent Diffusion and Hunting Cooperation (Journal of Nonlinear Modeling and Analysis, 2024)
This paper concerns a stationary prey-predator model with density-dependent diffusion and hunting cooperation under homogeneous Dirichletboundary conditions. Based on the spectral analysis, the asymptotic stability of trivial and semi-trivial solutions is obtained. Moreover, the sufficientconditions for the existence of positive solutions are established by using degree theory in cones. Our analytical results suggest that density-dependentdiffusion and hunting cooperation obviously influence on the positive solutions.
Keywords: Prey-predator model; density-dependent diffusion; hunting cooperation; positive solutions.