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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.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.612}, url = {http://global-sci.org/intro/article_detail/jnma/23352.html} }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.