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.
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)
