Hille-Yosida算子的非线性Lipschitz扰动  

Nonlinear Lipschitz Perturbation of Hille-Yosida Operators

作　　者：宋学力[1] 赵盼[1] 王小伟[1] 

机构地区：[1]长安大学理学院,西安710064

出　　处：《应用泛函分析学报》2015年第2期130-138,共9页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11201038);陕西省青年科技新星项目(2014KJXX-55);长安大学中央高校基本科研业务费专项资金项目(2013G2121017)

摘　　要：论文研究非自反Banach空间中Hille-Yosida算子的非线性Lipschitz扰动.首先,证明Hille-Yosida算子的非线性Lipschitz扰动诱导的微分方程的温和解构成非线性指数有界Lipschitz半群;其次,证明非线性扰动半群保持原半群的直接范数连续性质.获得的结果是线性算子半群某些结论的非线性推广.This paper is devoted to nonlinear Lipschitz perturbation of Hille-Yosda operators in non reflexive Banach spaces.Firstly,it proves that the mild solutions of the differential equations induced by nonlinear Lipschitz perturbation of Hille-Yosida operators compose nonlinear exponentially bounded Lipschitz semigroups;Secondly,it demonstrates that the nonlinear perturbed semigroups persist the immediate norm continuity of the original semigroups.The obtained results are the nonlinear extensions of some existing conclusions of the linear semigroups.

关 键 词：Hille-Yosida算子 非线性扰动 Lipschitz半群 直接范数连续性 

分 类 号：O177.91[理学—数学]