微分包含的稳定性

本文通过引用生存定理，Ｌｙａｐｕｎｏｖ第二方法和比较定理，首先证明了微分包含的整体存在定理，然后讨论了微分包含解的稳定性     

Banach空间中一类具阻尼的二阶微分包含的可控性

主要研究了Banach空间一类具有阻尼项的二阶微分包含的可控性,利用集值映射不动点定理,讨论了集值函数取凸值的情况,给出了微分包含可控性的充分条件.     

具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性

本文研究具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性.假设多值非线性和脉冲函数满足由非紧性测度表示的正则性条件,利用非紧性测度理论和多值凝聚不动点定理,得到这类微分包含的可控性的充分条件.     

Banach空间中微分包含解的存在性*

本文在无穷维Banach空间中讨论微分包含解的存在性,先给出了几个普通微分包含的比较定理,讨论了近似解与解的关系,然后得到了Banach空间中微分包含解的存在性定理.     

微分包含的周期生存轨道

对微分包含的周期生存轨道进行了研究讨论。首先给出微分包含生存问题的一约化性质;然后,利用投影微分包含的方法给出有限维空间中微分包含的周期生存轨道的一个存在性结果;在此基础上,利用Galerkin逼近方法得到Hilbert空间中偏微分包含周期生存轨道的存在性定理。     

关于微分包含的周期解及其应用

研究了一类发展包含的周期问题,其结果应用于建立一类半线性微分包含周期解的存在性定理．给出了半线性微分包含端点解的存在性定理和强松驰定理,并且应用于周期反馈控制系统．     

具约束的微分包含的极小时间函数

本文研究具状态约束Ｋ与目标集Ｃ之下的微分包含ｘ’（ｔ）∈Ｆ（ｘ（ｔ））的极小时间函数。主要证明了：⑴存在有限时间,使在约束Ｋ之下,微分包含的一条轨道可以到达Ｃ;⑵极小时间函数是下半连续的且是相依Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ方程的粘性上解。     

二阶非线性中立型无限时滞随机微分包含的可控性

本文主要在希尔伯特空间中讨论了二阶非线性中立型无限时滞随机微分包含的可控性问题.利用凝聚不动点定理得到了系统可控的一个充分性条件.     

关于生存定理的一个注记

研究多值映象F取无界值时微分包含生存轨道的存在性，证明了相应的生存定理．     

无穷维空间中非凸微分包含的生存构造及应用

本文在一般的Banach空间中研究非凸微分包含的生存问题．我们首先构造出了上述非凸微分包含的一个生存集．然后给出了所构造的生存集的两个应用．     

Stochastic differential inclusions and diffusion processes

Connections between weak solutions of stochastic differential inclusions and solutions of partial differential inclusions, generated by given set-valued mappings are considered. The main results are based on some continuous approximation selection theorem and weak compactness of the set of all weak solutions to a given stochastic differential inclusion.     

Chaotic solutions in differential inclusions: chaos in dry friction problems

The existence of a continuum of many chaotic solutions is shown for certain differential inclusions which are small periodic multivalued perturbations of ordinary differential equations possessing homoclinic solutions to hyperbolic fixed points. Applications are given to dry friction problems. Singularly perturbed differential inclusions are investigated as well.

     

Bifurcation of periodic solutions in differential inclusions

Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems.     

Differential Inclusions and Monotonicity Conditions for Nonsmooth Lyapunov Functions

In this paper we address the problem of characterizing the infinitesimal properties of functions which are nonincreasing along all the trajectories of a differential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous differential inclusions. Moreover, we show that the same criterion applies also in the case of Lipschitz continuous functions and continuous differential inclusions.     

Discretizations of Linear Elliptic Partial Differential Inclusions

Differential inclusions provide a suitable framework for modelling choice and uncertainty. In finite dimensions, the theory of ordinary differential inclusions and their numerical approximations is well-developed, whereas little is known for partial differential inclusions, which are the deterministic counterparts of stochastic partial differential equations.

The aim of this article is to analyze strategies for the numerical approximation of the solution set of a linear elliptic partial differential inclusion. The geometry of its solution set is studied, numerical methods are proposed, and error estimates are provided.     

Stochastic Invariance for Differential Inclusions

The aim of this paper is to combine two ways for representing uncertainty through stochastic differential inclusions: a 'stochastic uncertainty", driven by a Wiener process, and a 'contingent uncertainty", driven by a set-valued map. The paper is also devoted to the invariance of closed under stochastic differential inclusions with a Lipschitz right-hand side, characterized in terms of stochastic tangent sets to closed subsets.     

Nonconvex Differential Inclusions with Nonlinear Monotone Boundary Conditions

Existence results for problems with monotone nonlinear boundary conditions obtained in the previous publications by the author for functional differential equations are transferred to the case of nonconvex differential inclusions with the help of the selection theorem due to A. Bressan and G. Colombo.     

A Comparison between Two Theories for Multi-Valued Semiflows and Their Asymptotic Behaviour

This paper presents a comparison between two abstract frameworks in which one can treat multi-valued semiflows and their asymptotic behaviour. We compare the theory developed by Ball (1997) to treat equations whose solutions may not be unique, and that due to Melnik and Valero (1998) tailored more for differential inclusions. Although they deal with different problems, the main ideas seem quite similar. We study their relationship in detail and point out some essential technical problems in trying to apply Ball's theory to differential inclusions.     

Stochastic representation of partial differential inclusions

Partial differential inclusions of the form and ψ∈LFGu+cu, where LFG is a uniformly parabolic second order set-valued operator, are considered. In particular, basing on diffusions properties of weak solutions to stochastic differential inclusions, some existence and representation theorems for solutions of such type partial differential inclusions are given.     

Controllability of second-order neutral functional differential inclusions in Banach spaces

In this paper, we prove the controllability of second-order neutral functional differential inclusions in Banach spaces. The result are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for condensing maps due to Martelli.