平面双拉普拉斯算子嵌入特征值的扰动
Perturbations of embedded eigenvalues for the planar bilaplacian
摘要：
无界区域上的算子可以获得嵌入在本质谱中的特征值。确定这些嵌入的本征值的基础运营商的小扰动下的命运是一项具有挑战性的任务，和持久性的特性，这样的本征值是密切相关的本质谱的多重性。在本文中，我们考虑的平面bilaplacian与潜在的，并证明了一个嵌入的本征值持续存在的潜在的集合是局部的无限维流形与无限余维在适当的空间的潜力。
英文摘要：
Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the persistence properties of such eigenvalues is linked intimately to the multiplicity of the essential spectrum. In this paper, we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite-dimensional manifold with infinite codimension in an appropriate space of potentials.
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