非凸集值映射的包含切性及应用

本文在一般的Ｂａｎａｃｈ空间Ｘ中研究从非空闭集ＫＸ到Ｘ的非凸集值映射Ｆ的包含切性问题．得到的结果定理３．１把有关的结论推广到非光滑空间，定理３．３则将有限维空间的正则性定理推广到任意的Ｂａｎａｃｈ空间．作为结果的应用，我们证明了无穷维非凸微分包含和非凸控制系统生存解的存在性，且给出了一个方便的等价切性条件．     

具非凸右端项泛函微分包含的周期解

In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.     

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。     

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空间中一类二阶具阻尼项的积分-微分包含的可控性

本文讨论了一类二阶具阻尼项的积分-微分包含问题.利用集值不动点定理将问题转化为求不动点问题,进而得到系统可控性的充分条件.     

微分包含生存解集的拓扑性质

本文证明了有限维空间中微分包含系统的生存解集是一个Rδ-集，并将结果推广至无限维空间．     

集值映象不动点指数对微分包含与积分包含多解问题的应用

为获得一类微分包含与积分包含的多解存在性定理，我们应用集值映象不动点指数理论把著名的Ａｍａｎｎ三解定理等多解定理推广到集值映象，我们还用例子说明了所得结果．     

集值映射的连续不动点定理及其在微分包含中的应用

本首先证明了一类集值映射的下半连续性。在此基础上给出了Banach空间集值映射的一个连续不动点定理,作为应用,证明了一类微分包含解的存在性。这种方法是全新的。     

Banach空间中泛函微分包含的生存定理

本文研究可分Ｂａｎａｃｈ空间中泛函微分包含的解轨道的可生存性，建立了无限维空间中泛函微分包含的生存定理，其推论部分地回答了泛函微分方程中的一个开问题。     

Formulating Measure Differential Inclusions in Infinite Dimensions

Measure differential inclusions were introduced by J. J. Moreau to study sweeping processes, and have since been used to study rigid body dynamics and impulsive control problems. The basic formulation of an MDI is d / d (t) K(t) where is a vector measure, an unsigned measure, and K() is a set-valued map with closed, convex values and is hemicontinuous. Note that need not be absolutely continuous with respect to . Stewart extended Moreau's original concept (which applied only to cone-valued K()) to general convex sets, and gave strong and weak formulations of d / d (t) K(t) where K(t) R ⁿ . Here the strong and weak formulations of Stewart are extended to infinite-dimensional problems where K(t) X where X is a separable reflexive Banach space; they are shown to be equivalent under mild assumptions on K().     

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.     

Viability Theorems for Higher-Order Differential Inclusions

The aim of this paper is to establish both necessary and sufficient conditions for the existence of viable solutions of a higher-order differential inclusion. Higher-order tangent sets are introduced and studied to get such conditions. These tangent sets are analysed in the case of the viable set defined by equality or inequality constraints and viability conditions are rewritten in terms of these constraints.     

Existence of Solution of Nonlinear Neutral Stochastic Differential Inclusions with Infinite Delay

Abstract

This article is concerned with the existence of solution of nonlinear neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps due to Martelli.     

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.     

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.     

Existence of Solutions of Nonlinear Neutral Stochastic Differential Inclusions in a Hilbert Space

Abstract

In this paper, the existence of mild solutions of a class of non-linear neutral stochastic differential inclusions in Hilbert space is studied. The results are obtained by using a new fixed point theorem for a condensing map due to Martelli. For an application of the result, the neutral stochastic reaction-diffusion inclusion is also discussed.     

Controllability of Neutral Functional Differential and Integrodifferential Inclusions with Infinite Delay

Sufficient conditions are derived for the controllability of neutral functional differential and integrodifferential inclusions with infinite delay in a Banach space. The results are obtained by using a fixed-point theorem for condensing maps due to Martelli. An example is given to illustrate the results.