This paper is concerned with a Lotka-Volterra model with nonlinear cross diffusion. The global existence of generalized solutions is established under some proper assumptions, and the nonexistence of nonconstant solutions is also investigated when diffusion rate is sufficiently large. At the same time, sufficient conditions ensuring the existence of non-constant solutions are obtained by using Leray-Schauder degree theory. Furthermore, steady-state bifurcation analysis is carried out in details by using Lyapunov-Schmidt reduction.

中文翻译：

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具有非线性交叉扩散的Lotka-Volterra竞争模型的稳态

本文涉及具有非线性交叉扩散的Lotka-Volterra模型。在某些适当的假设下建立了广义解的全局存在性，并且当扩散率足够大时，还研究了非恒定解的不存在性。同时，通过使用Leray-Schauder度数理论获得了确保存在非恒定解的充分条件。此外，使用Lyapunov-Schmidt归约法对稳态分叉进行了详细分析。