具有非线性交叉扩散的Lotka-Volterra竞争系统的共存解

Coexistence Solutions of Lotka-Volterra Competitive Systems with Nonlinear Cross Diffusion

考虑一类齐次Dirichlet边界条件下具有非线性交叉扩散的Lotka-Volterra竞争系统的共存解问题.首先,借助线性算子的谱理论分析该问题平凡解和半平凡解的稳定性;其次,利用正锥上的不动点指数理论给出该问题共存解存在的充分条件.

We considered the coexistence solution problem of a class of Lotka-Volterra competitive systems with nonlinear cross-diffusion under homogeneous Dirichlet boundary conditions.Firstly,the stability of trivial solutions and semi-trivial solutions of the problem was analyzed by using spectral theory of linear operators.Secondly,sufficient conditions for the existence of coexistence solutions of the problem were given by using the fixed point index theory on positive cone.