Abstract
This paper is concerned with a Lotka–Volterra model with density-dependent motion. Under homogeneous Dirichlet boundary conditions, which is different from the previous article (Liu and Guo, 2021), the corresponding steady-state problem is discussed. Stability properties of the trivial and semitrivial solutions are determined completely. The sufficient conditions for the existence of coexistence solutions are also obtained by using the theory of fixed point index in positive cones. Finally, the limiting behavior of coexistence solutions is studied as some certain parameter tends to infinity.
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