【摘要】 研究有界线性算子强连续半群在非线性Lipschitz扰动下的正则性质保持问题.具体地,我们证明:如果强连续半群是直接范数连续的,则非线性扰动半群是直接Lipschitz范数连续的.结论推广了线性算子半群的范数连续性质保持,丰富和完善了非线性算子半群的理论.更多还原

【Abstract】 The paper is devoted to property persistence of strongly continuous semigroups of linear bounded operators under Lipschitz perturbations.Particularly,we prove that the nonlinearly perturbed semigroup is immediately Lipschitz norm continuous if the linear strongly continuous semigroup is immediately norm continuous.The result derived extends persistence of norm continuity of linear strongly continuous semigroups and enriches theory of semigroups of nonlinear operators.更多还原