Co—半群关于参数的可微性及其应用

考虑了Co-半群关于参数的可微性,而参数含在半群在无穷小生成元中,证明了：无穷小生成元关于参数的广义连续性及强可微性蕴含着Co-半群关于参数的可微性。这些结果被应用于证明线性延滞微分方程的解关于延滞量的可微性质。     

双参数 C-半群

引入单参数C-半群和双参数C0-半群,给出了更一般的双参数C-半群和无穷小生成元的定义,应用双参数半群与单参数半群的关系和双参数半群的性质,给出了双参数C-半群的阶全微分,偏微分,指数有界性,和双参数C-半群是由C、A1和A2唯一确定的闭稠定线性算子的一个充分条件.     

Lq(Ω)空间中C0-半群的一些结果

设T（t）是Lq（1＜q＜∞）空间上的C0-半群,A为其无穷小生成元．本文证明若T（t）是弱LP稳定的,则其生成元的谱界是负的。由LotzWeis最近得到的关于Lq（Ω）空间中正C0半群的增长界等于生成元的谱界这一结果得出,Lq（Ω）空间中正C0半群弱Lp稳定与指数稳定等价．     

算子半群母元豫解式的增长阶和它的指数稳定性

设X为Banach空间,T(t)为X上的(1,A)类半群,A为T(t)的无穷小母元,若对每个x∈X,映射t→T(t)x关于t>t_0可微,则称T(t)关于t>t_0可微,本文讨论了关于t>t_0可微的(1,A)类半群的若干性质,并利用可微半群母元豫解式的增长阶特征证明了关于t>t_0可微的(1,A)类半群是指数稳定的充分必要条件为sup{Reλ:λ∈σ(A)}<0.     

关于非线性Lipschitz算子半群生成元的存在性

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.     

Hilbert空间中耗散算子的性质研究

文章研究了Hilbert空间中耗散算子的性质,并给出此类算子成为C0压缩半群无穷小生成元的一些条件。     

Hamilton算子矩阵的半群生成定理

研究了Hamilton算子矩阵的半群生成问题,得到其生成C_0半群的若干充分必要条件,并给出其成为半群无穷小生成元时的谱分布.作为应用,基于Hamilton系统的半群方法,给出一类四阶微分方程混合问题的古典解.     

人口半群的可微性质

本文通过无穷小母元的谱性质讨论人口半群的性质,证明了:存在 t_0>0,当 t>t_0时,人口半群{T(t)|t≥0)}是可微的.在一个安定的社会中,人口密度函数 P(r,t)满足偏微分方程     

半线性中立型分数阶微分方程S-渐近ω周期解

在Banach空间X中,研究了如下半线性Caputo-分数阶中立型微分方程S-渐近w周期解的存在性其中0α1,-A是解析半群{T(t)}_(t≥0)的无穷小生成元.     

半群的拟紧性和不可约性

利用算子半群生成元的边界扰动方法,给出了Banach格上C0半群的拟紧性和不可约性的充分条件.并利用该结果对一串联可修复系统的拟紧性和不可约性进行了研究.     

An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C0-Semigroups

We consider a system of two semilinear differential inclusions with infinitesimal generators of C ₀-semigroups. The nonlinear terms are of high frequency with respect to time and periodic with a specified period. Moreover, they are condensing in the state variables (x,y) with respect to a suitable measure of noncompactness. The goal of the paper is to give sufficient conditions to guarantee, for >0 sufficiently small, the existence of periodic solutions and to study their behaviour as 0. The main tool to achieve this is the topological degree theory for uppersemicontinuous, condensing vector fields.     

An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C 0-Semigroups

We consider a system of two semilinear differential inclusions with infinitesimal generators of C ₀-semigroups. The nonlinear terms are of high frequency with respect to time and periodic with a specified period. Moreover, they are condensing in the state variables (x,y) with respect to a suitable measure of noncompactness. The goal of the paper is to give sufficient conditions to guarantee, for ∈>0 sufficiently small, the existence of periodic solutions and to study their behaviour as ∈→0. The main tool to achieve this is the topological degree theory for uppersemicontinuous, condensing vector fields.     

Differentiability of solutions of second-order functional differential equations with unbounded delay

In this paper we study the differentiability of solutions of the second-order semilinear abstract retarded functional differential equation with unbounded delay, specially when the underlying space is reflexive or at least has the Radon–Nikodym property. We apply our results to characterize the infinitesimal generators of several strongly continuous semigroups of linear operators that arise in the theory of linear abstract retarded functional differential equations with unbounded delay on a phase space defined axiomatically.     

Decay estimates of functions through singular extensions of vector-valued Laplace transforms

Let X be a Banach space and let f∈L^∞(R⁺;X) whose Laplace transform extends analytically to some region containing iR?{0}, possibly having a pole at the origin. In this paper, we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its Laplace transform along the imaginary axis. This technique is applied to obtain decay estimates of smooth orbits of bounded C₀-semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum. These results are close to those given recently by C.J.K. Batty and T. Duyckaerts.     

抽象空间中非时齐马氏过程的分析理论(Ⅱ)——非时齐马氏过程与双参数半群

本文是[1]的续篇,一切符号及定义均沿袭[1].为省篇幅,不再重述.     

Poincaré and Opial inequalities for vector-valued convolution products

Various L^p$L^p$ form Poincaré and Opial inequalities are given for vector-valued convolution products. We apply our results to infinitesimal generators of _C0$C_0$-semigroups and cosine functions. Typical examples of these operators are differential operators in Lebesgue spaces.     

A note on the comparison of Co-semigroups

If S(.) and T(.) are two C_o-semigroups of linear operators on a Banach space X, we derive a characterization of their generators so that ||S(t)−T(t)||=O(t) as t→O⁺.     

On Some Functions That Send Each Generator of a C0-Semigroup to the Generator of a Holomorphic Semigroup

We give some conditions on functions of the Schoenberg class T for them to send the generators of uniformly bounded semigroup of class C ₀ to the generators of holomorphic semigroups. This generalizes Yosida, Balakrishnan, and Kato's result relating to fractional powers of operators. The functional calculus of generators of C ₀-semigroups which uses the class T was constructed in the preceding articles of the author.