作 者: ;
机构地区: 西安交通大学理学院应用数学研究中心
出 处: 《应用泛函分析学报》 2005年第1期39-45,共7页
摘 要: 基于作者先前提出的Lipschitz对偶思想,对非线性Lipschitz算子半群引入了若干Lipschitz对偶概念,得到了一类非线性Lipschitz算子半群存在生成元的特征刻画.这一结果直接将关于C0-半群如下结论推广到了非线性情形:C0-半群具有有界生成元当且仅当它一致连续. This paper is concerned with the existence of generator of Lipschitzian semigroup. By developing some novel dual notions related to Lipschitzian semigroup, a necessary and sufficient condition for the existence of generator of Lipschitzian semigroup is proved. This obtained result is a nonlinear generalization of the well-known theorem that a C_0-semigroup is uniformly continuous if and only if its generator is bounded.