We prove an abstract and flexible continuation theorem for zeros of parametrized Fredholm maps between Banach spaces. It guarantees not only the existence of zeros to corresponding equations, but also that they form a continuum for parameters from a connected manifold. Our basic tools are transfer maps and a specific topological degree. The main result is tailor‐made to solve boundary value problems over infinite time‐intervals and for the (global) continuation of homoclinic solutions.

中文翻译：

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弗雷德霍尔姆地图的延续原理I：理论与基础

我们证明了Banach空间之间参数化Fredholm映射的零点的抽象且灵活的连续定理。它不仅保证了对应方程式的零点的存在，而且还保证了零点点构成了相连歧管中参数的连续体。我们的基本工具是传输图和特定的拓扑度。主要结果是量身定制的，可以解决无限时间间隔内的边值问题，并且可以实现（整体）同宿解。