The purpose of this note is to study the existence of a nontrivial solution for an elliptic system which comes from a newly introduced mathematical problem so called Field-Road model. Specifically, it consists of coupled equations set in domains of different dimensions together with some interaction of non classical type. We consider a truncated problem by imposing Dirichlet boundary conditions and an unbounded setting as well.

中文翻译：

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关于特殊环境中相互作用物种传播的一些模型问题

本文的目的是研究椭圆系统的一个非平凡解的存在，该解来自一个新引入的数学问题，即所谓的Field-Road模型。具体来说，它由在不同维度的域中设置的耦合方程式以及一些非经典类型的相互作用组成。我们通过施加Dirichlet边界条件和无界设置来考虑一个截断的问题。