Generalized Vector Equilibrium Problems with Trifunctions

In this paper, we study the existence of strong and weak solutions of the generalized vector equilibrium problems for trifunctions. Two special classes of vector-valued trifunctions are introdcued, called the classes of (SPM) and (GPM), respectively. Some existence results for strong solutions associated to functions of these classes are given.     

Existence theorems via duality for equilibrium problems with trifunctions

We present an existence result for an equilibrium problem formulated with trifunctions, which is motivated by variational inequalities governed by quasimonotone operators. To prove the existence result, we define the dual problem, and some monotonicity notions for trifunctions. From the main result follow, among others, the Browder–Minty theorem for variational inequalities and Ky Fan’s Minimax theorem. Some applications for mixed equilibrium problems and variational inequalities are given.     

Existence of positive solutions of (p(x),q(x))-Laplacian parabolic systems with right hand side defined as a multiplication of two separate functions

The paper deals with the study of the existence of weak positive solutions for a new class of the system of parabolic differential equations with respect to the symmetry conditions by using sub-super solutions method. Our results are natural extensions from our previous ones in (Bol. Soc. Mat. Mex. 2019; 25:145-162) and (Appl. Math E-Notes. 2018; 18:209-218), where we have already studied the existence of positive solutions for some classes of Laplacian elliptic problems by using one classical method.     

Optimum solutions for a system of differential equations via measure of noncompactness

New classes of mappings, called cyclic (noncyclic) condensing operators, are introduced and used to investigate the existence of best proximity points (best proximity pairs) with the help of a suitable measure of noncompactness. In this way, we obtain some real generalizations of Schauder and Darbo’s fixed point theorems. In the last section, we apply such results to study the existence of optimum solutions to a system of differential equations.     

On quasilinear parabolic equations which admit global solutions for initial data with unrestricted growth

Three classes of quasilinear parabolic equations which have the common feature that their principal coefficients decay as the solution or its gradient blows up are studied. Long time existence of solutions for their Cauchy problems for initial data with arbitrary growth is established. Received September 9, 1999 / Accepted May 9, 2000 / Published online September 14, 2000     

On F-Implicit Generalized Vector Variational Inequalities

In this paper, we study the F-implicit generalized (weak) case for vector variational inequalities in real topological vector spaces. Both weak and strong solutions are considered. These two sets of solutions coincide whenever the mapping T is single-valued, but not set-valued. We use the Ferro minimax theorem to discuss the existence of strong solutions for F-implicit generalized vector variational inequalities.     

Ultradifferentiable extension theorems: A survey

We survey ultradifferentiable extension theorems, i.e., quantitative versions of Whitney’s classical extension theorem, with special emphasis on the existence of continuous linear extension operators. The focus is on Denjoy–Carleman classes for which we develop the theory from scratch and discuss important related concepts such as (non-)quasianalyticity. It allows us to give an efficient and, to a fair extent, elementary introduction to Braun–Meise–Taylor classes based on their representation as intersections and unions of Denjoy–Carleman classes.     

On the theorem of T. Yamada and S. Watanabe

The well-known theorem of T. Yamada and S. Watanabe asserts that (weak) existence and pathwise uniqueness of the solution of a stochastic equation implies the existence of a strong solution. This is the most powerful tool for proving that a stochastic equation possesses a strong solution. However, pathwise uniqueness is far from being a necessary condition for this. Even if the solution is not unique in law it is also of interest to ask for strong solutions. In the present note, we will discuss in more detail the connection between pathwise uniqueness and the existence of a strong solution. We will state a condition which is not only sufficient but also necessary for the existence of a strong solution.     

随机微分方程的强解

在这篇文章中我们通过一种去掉扩散系数的变换证明了随机微分方程强解的存在唯一性.     

Studies on anti‐periodic boundary value problems for two classes of special second order impulsive differential equations

We consider anti‐periodic boundary value problems for two classes of special second order impulsive differential equations. On the basis of several important impulsive differential inequalities, by using the monotone iterative technique coupled with lower and upper solutions, we obtain sufficient conditions to guarantee the existence and uniqueness of solutions for such problems. Further, we give two examples to illustrate our conclusions. Copyright © 2013 John Wiley & Sons, Ltd.     

临界半线性双调和方程非平凡解的存在性

该文借助于没有PS条件的翻山引理，并利用Sobolev嵌入的最佳达到函数，克服了由于Sobolev嵌入失紧性而带来的系列困难．证明了含临界增长的两类观调和方程边值问题非平凡解的存在性．     

一般有界区域上次线性椭圆方程改进的正解估计

在一般有界区域上，建立了次线性椭圆方程广义Ｄｉｒｉｃｈｌｅｔ问题改进的正解估计和有界强解的存在性定理．     

Symmetry classes of tensors and semi-direct product of finite abelian groups

In the study of symmetry classes of tensors, finding examples of symmetry classes of tensors that possess an o*-basis is of considerable interest. There are only few classes of groups that have been provided a necessary and sufficient condition for having such a basis. There is no general criterion for any finite group yet. In this note, we provide a necessary and sufficient condition for the existence of o*-basis of symmetry classes of tensors associated with semi-direct product of some finite abelian groups and, consequently, their wreath product.     

Some logical metatheorems with applications in functional analysis

In previous papers we have developed proof-theoretic techniques for extracting effective uniform bounds from large classes of ineffective existence proofs in functional analysis. Here `uniform' means independence from parameters in compact spaces. A recent case study in fixed point theory systematically yielded uniformity even w.r.t. parameters in metrically bounded (but noncompact) subsets which had been known before only in special cases. In the present paper we prove general logical metatheorems which cover these applications to fixed point theory as special cases but are not restricted to this area at all. Our theorems guarantee under general logical conditions such strong uniform versions of non-uniform existence statements. Moreover, they provide algorithms for actually extracting effective uniform bounds and transforming the original proof into one for the stronger uniformity result. Our metatheorems deal with general classes of spaces like metric spaces, hyperbolic spaces, CAT(0)-spaces, normed linear spaces, uniformly convex spaces, as well as inner product spaces.

     

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.     

(NCI)算子与(NFI)算子

引入两类与不变子空间密切相关的算子,即(NCI)算子与(NFI)算子.考虑这两类算子的性质,例如存在性,相似不变性,以及与强不可约算子的关系等.并在可分Banach空间上讨论谱为单点集{0}的算子能否小紧摄动成为(NFI)算子.     

On tertiary exotic characteristic classes

We prove the existence and nontriviality of tertiary exotic characteristic classes extending the results of Peterson and Ravenel for secondary exotic classes.

     

投资的收益和风险的数学模型及算法研究

本文按照“满意解”、“多组解”的思路对投资的收益和风险问题进行了分析和处理 ,提出了将净收益与总体风险划分为若干等级 ,并按等级求出多组满意解的思想方法 ,最后对模型的数学性质与计算方法进行了初步研究     

Existence and uniqueness of pseudo-almost periodic solutions to some classes of partial evolution equations

Some sufficient conditions for the existence and uniqueness of pseudo-almost periodic (mild) solutions to some classes of partial evolution equations are given. We then make use of our abstract results to discuss the existence of pseudo-almost periodic solutions to some partial differential equations.     

Categoricity in multiuniversal classes

The third author has shown that Shelah's eventual categoricity conjecture holds in universal classes: class of structures closed under isomorphisms, substructures, and unions of chains. We extend this result to the framework of multiuniversal classes. Roughly speaking, these are classes with a closure operator that is essentially algebraic closure (instead of, in the universal case, being essentially definable closure). Along the way, we prove in particular that Galois (orbital) types in multiuniversal classes are determined by their finite restrictions, generalizing a result of the second author.