论文标题
与希尔伯特空间中的线性特征值问题以及非线性光谱理论相关的程度
A degree associated to linear eigenvalue problems in Hilbert spaces and applications to nonlinear spectral theory
论文作者
论文摘要
我们扩展到无限的维度上下文。作者最近强调的两个完全不同的主题之间的链接是：真实平方矩阵的经典特征值问题和在方向有限的尺寸真实歧管之间的地图之间的图。多亏了这一扩展，我们解决了我们在最近的文章中提出的非线性光谱理论中全球延续的猜想。我们的结果（前猜想）用于证明溶液对含有空气抗性摩擦力的扰动运动方程的rabinowitz型全球延续性。
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.
