Abstract

Based on the recent development of the theory of measures of noncompactness, we first show a representation theorem of measures of noncompactness defined on Banach spaces. Then, in terms of measure of noncompactness, we present some new characterizations of the existence of global attractors for norm-to-weak continuous semigroups, and a fixed point theorem for norm-to-weak continuous mappings.

中文翻译：

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非紧致性度量及其在算子半群全局吸引子上的应用

摘要

基于非紧致性度量理论的最新发展，我们首先展示了在Banach空间上定义的非紧致性度量的表示定理。然后，根据非紧致性的度量，我们给出了常态至弱连续半群全局吸引子存在的一些新特征，以及常态至弱连续映射的不动点定理。