Abstract By means of a suitable degree theory, we prove persistence of eigenvalues and eigenvectors for set-valued perturbations of a Fredholm linear operator. As a consequence, we prove existence of a bifurcation point for a non-linear inclusion problem in abstract Banach spaces. Finally, we provide applications to differential inclusions.

中文翻译：

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具有集值扰动的 Fredholm 算子的特征值问题

摘要 通过合适的度理论，我们证明了Fredholm 线性算子集值扰动的特征值和特征向量的持久性。因此，我们证明了抽象 Banach 空间中非线性包含问题的分岔点的存在。最后，我们提供了微分夹杂物的应用。