In this paper we use the homotopy invariants methods to study the global dynamics of the reaction–diffusion systems that are at resonance at infinity. Considering degrees of the resonance for the nonlinear perturbation we establish Landesman–Lazer type conditions and use them to express the Rybakowski–Conley index of the invariant set consisting of all bounded solutions. Obtained results are applied to study the existence of solutions connecting stationary points for the system of nonlinear heat equations.

中文翻译：

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关于共振反应扩散系统的整体动力学

在本文中，我们使用同伦不变式方法研究在无限远处共振的反应扩散系统的整体动力学。考虑非线性扰动的共振程度，我们建立了Landesman–Lazer型条件，并用它们来表示由所有有界解组成的不变集的Rybakowski–Conley指数。将获得的结果用于研究非线性热方程组的连接固定点的解的存在性。