Abstract

A differential inclusion whose right-hand side is the sum of two set-valued mappings in a separable Banach space is considered. The values of the first mapping are bounded and closed but not necessarily convex, and this mapping is Lipschitz continuous in the phase variable. The values of the second one are closed, and this mapping has mixed semicontinuity properties: given any phase point, it either has closed graph and takes a convex value at this point or is lower semicontinuous in its neighborhood. Under additional assumptions related to measurability and growth conditions, the existence of a solution is proved.

中文翻译：

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Banach空间中具有混合半连续性的微分包含

摘要

考虑了一个微分包含，其右手边是可分离的Banach空间中两个集合值映射的总和。第一个映射的值是有界和封闭的，但不一定是凸的，并且此映射在相位变量中是Lipschitz连续的。第二个值的值是封闭的，并且此映射具有混合的半连续性：给定任何相位点，它要么具有封闭的图，并在该点采用凸值，要么在其附近较低半连续。在与可测量性和增长条件有关的其他假设下，证明了解的存在。