We extend to the infinite dimensional context the link between two completely different topics recently highlighted by the authors: the classical eigenvalue problem for real square matrices and the Brouwer degree for maps between oriented finite dimensional real manifolds. Thanks to this extension, we solve a conjecture regarding global continuation in nonlinear spectral theory that we have formulated in a recent article. Our result (the ex conjecture) is applied to prove a Rabinowitz type global continuation property of the solutions to a perturbed motion equation containing an air resistance frictional force.

中文翻译：

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Hilbert空间中与线性特征值问题相关的度及其在非线性谱理论中的应用

作者最近强调了两个完全不同的主题之间的联系：无穷维上下文：实平方矩阵的经典特征值问题和定向有限维实流形之间的映射的Brouwer度。由于有了这一扩展，我们解决了最近一篇文章中提出的关于非线性谱理论中全局连续性的一个猜想。我们的结果（前猜想）用于证明包含空气阻力摩擦力的扰动运动方程解的Rabinowitz型全局连续性。