In this paper, we study the existence of positive solutions for a class of reaction–diffusion equations in spatially heterogeneous environment. We also determine the asymptotic profiles of positive solutions when some parameter goes to zero. Our analytical results suggest that the spatial heterogeneity has obvious influence on the positive solutions.

中文翻译：

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空间异质环境中一类反应扩散方程的正解

在本文中，我们研究了空间异质环境中一类反应扩散方程的正解的存在性。当某些参数变为零时，我们还确定正解的渐近曲线。我们的分析结果表明，空间异质性对正解具有明显的影响。