A stage-structure competition-diffusion model with spatial heterogeneity is investigated in this paper. Under some suitable assumptions, the existence of spatially non-homogeneous steady-state solutions is established by investigating eigenvalue problems with indefinite weight and employing Lyapunov-Schmidt reduction. The stability of spatially nonhomogeneous steady-state solutions is obtained by analyzing the set of the spectrum of the associated infinitesimal generator. In particular, the global stability of the steady-state solutions is described in weak competition case.

中文翻译：

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具有空间异质性的舞台结构模型稳定性分析

本文研究了具有空间异质性的阶段结构竞争扩散模型。在一些合适的假设下，通过研究具有不确定权重的特征值问题并采用 Lyapunov-Schmidt 约简，建立了空间非齐次稳态解的存在性。空间非齐次稳态解的稳定性是通过分析相关无穷小发生器的频谱集获得的。特别是在弱竞争情况下描述了稳态解的全局稳定性。