一类广义非线性混合拟变分包含组

本文引入了一类新的带松弛单调映射和松弛Lipschitz映射的广义非线性混合拟变分包含组 ,构造了求解该类变分包含组的迭代算法 ,证明了该类变分包含组解的存在性以及由本文构造的迭代算法产生的迭代序列的强收敛性 .所得结果推广和改进了大量文献中的最新结果[1 5 ] .     

Banach空间无界时滞的脉冲发展中立泛函积分微分包含的存在性

本文建立了Banach空间中无界时滞的脉冲发展中立泛函积分微分包含温和解存在的充分条件，我们利用由Dhage建立的多值混合不动点定理与发展系统证明了解的存在性．     

Nonemptiness of viability kernels for infinite-dimensional differential inclusions

We investigate infinite-dimensional differential inclusions. Sufficient conditions for nonemptiness of the viability kernels of such systems are obtained.     

Banach空间内一类含松弛-(H,η)-调算子的广义混合拟似变分包含组

在Banach空间内,引入和研究了一类新的含松弛-(H,η)-单调算子的广义混合拟似变分包含组.利用松弛-(H,η)-单调算子的豫解算子技巧,给出了求这类广义混合拟似变分包含组近似解的一个新逼近算法,并证明了由这个新算法生成的迭代序列强收敛于该变分包含组的精确解.文章结果改进与推广了近期文献中的相应结果.     

一类含参广义集值拟变分包含组的解的灵敏性分析

本文引入了一类新的含参广义集值拟变分包含组,应用隐预解算子技巧,建立了该类变分包含组与一类不动点问题的等价性,在适当的条件下,分析了含参广义集值拟变分包含组的解的灵敏性,所得结果推广改进了最新文献中的许多结果．     

Variational Inclusions for Fuzzy Mappings

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｄｄｉｑｉａｎｄＡｎｓａｒｉ［４］ｄｅｖｅｌｏｐｅｄｉｔｅｒａｔｉｖｅａｌｇｏｒｉｔｈｍｓｆｏｒｆｉｎｄｉｎｇａｐｐｒｏｘｉｍａｔｅｓｏｌｕｔｉｏｎｔｏｎｅｗｃｌａｓｓｅｓｏｆｑｕａｓｉｖａｒｉａｔｉｏｎａｌｉｎｅｑｕａｌｉｔｉｅｓｉｎＨｉｌｂｅｒｔｓｐａｃｅｓ，ＨａｓｓｏｕｎｉａｎｄＭｏｕｄａｆｉ［１］ｅｘｔｅｎｄｔｈｅｍａｉｎｉｄｅａｓｏｆｐａｐｅｒ［４］ｔｏｍｏｒｅｇｅｎｅｒａｌｃａｓｅｓ，ｗｈｉｃｈｃｏｎｓｉｄｅｒｅｄａｃｌａｓｓｏｆｖａｒｉａｔｉｏｎ…     

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.     

Banach空间中随机微分包含的弱解存在性定理

本文对Banach空间中的微分包含及随机微分包含引入了弱解的概念,并给出了它们的存在性定理。     

一类(H,η)-单调算子的变分包含组

在Hilbert空间中,引入并研究一类新的关于(H,η)-单调算子的广义变分包含组问题.利用预解算子技巧和不动点定理证明了这类变分包含组解的存在性和唯一性.     

On Global Attractors of Multivalued Semiprocesses and Nonautonomous Evolution Inclusions

In this paper we define multivalued semiprocesses and give theorems providing the existence of global attractors for such systems. This theory generalizes the construction of nonautonomous dynamical systems given by V. V. Chepyzhov and M. I. Vishik to the case where the system is not supposed to have a unique solution for each initial state. Further, we apply these theorems to nonautonomous differential inclusions of reaction–diffusion type.     

System of generalized resolvent equations with corresponding system of variational inclusions

The purpose of this paper is to introduce a new system of generalized resolvent equations with corresponding system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between system of generalized resolvent equations and system of variational inclusions. The iterative algorithms for finding the approximate solutions of system of generalized resolvent equations are proposed. The convergence of approximate solutions of system of generalized resolvent equations obtained by the proposed iterative algorithm is also studied.      

对带误差项的广义集值变分包含的近似点算法

研究一类新的广义集值变分包含：０∈Ｎ（ｗ,ｙ）＋Ａ（ｚ,ｕ）,它包合了近几年许多作者所作的变分包合问题．在实Ｈｉｌｂｅｒｔ空间中,利用极大单调算子的性质,建立了广义集值变分包合和不动点问题间的等价性．利用这种等价性,建立了一些摄动迭代算法,并证明了近似解序列强收敛于精确解．本文的算法和结果改进和一般化了最近许多文章中相应的算法和结果．     

Convergence of Iterative Schemes for Multivalued Quasi-Variational Inclusions

Relying on the resolvent operator method and using Nadler's theorem, we suggest and analyze a class of iterative schemes for solving multivalued quasi-variational inclusions. In fact, by considering problems involving composition of mutivalued operators and by replacing the usual compactness condition by a weaker one, our result can be considered as an improvement and a significant extension of previously known results in this field.     

Antiplane shear of a strip containing a staggered array of rigid line inclusions

Motivated by the increased use of fibre-reinforced materials, we illustrate how the effective elastic modulus of an Isotropic and homogeneous material can be increased by the insertion of rigid inclusions. Specifically, we consider the two-dimensional antiplane shear problem for a strip of material. The strip is reinforced by introducing two sets of ribbon-like, rigid inclusions perpendicular to the faces of the strip. The strip is then subjected to a prescribed uniform displacement difference between its faces, see Figure 1. It should be noted that the problem posed is equivalent to that of the uniform antiplane shear problem for an infinite two-dimensional material containing a staggered array of rigid inclusions (see [1] for a review of antiplane problems in the literature). The problem is reduced in standard fashion [2–6] to a mixed boundary value problem in a rectangular domain, whose closed form solution given in terms of integrals of Weierstrassian Elliptic functions, is obtained via triple sine series techniques. The effective shear modulus of the reinforced strip can now be calculated and compared with the shear modulus of a strip without inclusions. Also obtained are the stress singularity factors at the end tips of the inclusions. Numerical results are presented for several different reinforcement geometries.     

Existence and iterative approximation of solutions of a system of general variational inclusions

In this paper, we consider a system of general variational inclusions in q-uniformly smooth Banach spaces. Using proximal-point mapping technique, we prove the existence and uniqueness of solution and suggest a Mann type perturbed iterative algorithm for the system of general variational inclusions. We also discuss the convergence criteria and stability of Mann type perturbed iterative algorithm. The techniques and results presented here improve the corresponding techniques and results for the variational inequalities and inclusions in the literature.     

Extremality,Controllability, and Abundant Subsets of Generalized Control Systems

The generalized control system that we consider in this paper is a collection of vector fields, which are measurable in the time variable and Lipschitzian in the state variable. For such system, we define the concept of an abundant subset. Our definition follows the definition of an abundant set of control functions introduced by Warga. We prove a controllability–extremality theorem for generalized control systems, which says, in essence, that either a given trajectory satisfies a type of maximum principle or a neighborhood of the endpoint of the trajectory can be covered by trajectories of an abundant subset. We apply the theorem to a control system in the classical formulation and obtain a controllability–extremality result, which is stronger, in some respects, than all previous results of this type. Finally, we apply the theorem to differential inclusions and obtain, as an easy corollary, a Pontryagin-type maximum principle for nonconvex inclusions.     

Implicit resolvent dynamical systems for quasi variational inclusions

In this paper, we suggest and analyze a class of implicit resolvent dynamical systems for quasi variational inclusions by using the resolvent operator technique. We show that the trajectory of the solution of the implicit dynamical system converges globally exponentially to the unique solution of the quasi variational inclusions. Our results can be considered as a significant extension of the previously known results.     

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.     

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.     

实$q$-一致光滑Banach空间中一类新的涉及广义 增生映射的集值变分包含组的近似可解性

A new system of set-valued variational inclusions involving generalized H(·, ·)-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operator technique associated with H(·, ·)-accretivity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.