(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
This paper concerns a stationary prey-predator model with density-dependent diffusion and hunting cooperation under homogeneous Dirichlet boundary conditions. Based on the spectral analysis, the asymptotic stability of trivial and semi-trivial solutions is obtained. Moreover, the sufficient conditions for the existence of positive solutions are established by using degree theory in cones. Our analytical results suggest that density-dependent diffusion and hunting cooperation obviously influence on the positive solutions.