Solutions of Ginzburg-Landau equations with weight and minimizers of the renormalized energy

In this paper, it is proved that for any given d non-degenerate local minimum points of the renormalized energy of weighted Ginzburg-Landau eqautions, one can find solutions to the Ginzburg-Landau equations whose vortices tend to these d points. This provides the connections between solutions of a class of Ginzburg-Landau equations with weight and minimizers of the renormalized energy.     

多目标规划的ακ—较多有效性

本文先讨论带两个参数的ακ－较多锥的个性质，借助它们研究了多目标规划问题的ακ－较多有效解和ακ－较多最优解之间以及它们与Pareto有效解之间的关系，同时，还各自给出这两类解存在的两个充要条件。     

ALMOST PERIODICITY FOR AN IMPULSIVE PURE DELAY LOGISTIC EQUATION

By employing a fixed point theorem in cones,we investigate the existence of almost periodic solutions to an impulsive pure delay Logistic equation. A set of suffcient conditions for the existence of almost periodic solutions to the equation are obtained.     

一类二阶m点边值问题的正解

Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.     

MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRDINGER SYSTEMS

We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in RN . We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.     

MULTIPLE POSITIVE SOLUTIONS OF NONRESONANT SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

This paper studies the existence of multiple positive solutions of nonresonant singular boundary value problem of second order ordinary differential equations. A sufficient condition for the existence of C[0,1] multiple positive solutions as well as C1[0, 1] multiple positive solutions is given by means of the fixed point theorems on cones.     

NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS

Let(E, ξ) = ind(En, ξn) be an inductive limit of a sequence(En, ξn)n∈N of locally convex spaces and let every step(En, ξn) be endowed with a partial order by a pointed convex(solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces,the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence(Sn)n∈N of ordering cones is nonconflicting, an existence theorem on lastingly weakly efficient points is presented. From this,an existence theorem on lastingly globally properly efficient points is deduced.     

EXISTENCE OF POSITIVE SOLUTION TO NONLINEAR STURM-LIOUVILLE SINGULAR BVP

In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.     

MULTIPLE POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF DELAY DIFFERENTIAL EQUATIONS WITH DENUMBERABLE SINGULARITIES ON INFINITE INTERVAL

This paper deals with the existence of denumberable positive solutions to boundary value problems of delay differential equations with denumberable singularities on infinite intervals. By the fixed-point index theory and a new fixed-point theorem in cones, the existence of denumberable positive solutions is obtained under some suitable growth conditions imposed on the nonlinear term.     

带有拉普拉斯算子的离散分数阶边值问题解的存在性

By establishing the corresponding variational framework, and using the critical points theorem, we give the existence of multiple solutions for a fractional difference boundary value problem with p-Laplacian operator. Under some suitable assumptions we obtain the existence of a positive parameter such that the problem admits at least three solutions. Some examples are presented to illustrate the main results.     

一类反应扩散方程正解的存在性

本文使用锥映象不动点指数方法,讨论了一类反应扩散方程正解的存在性.     

Cone Characterizations of Approximate Solutions in Real Vector Optimization

Approximate nondominated solutions of real vector optimization problems are characterized using the concept of translated cones. Relationships between these solutions and Pareto nondominated points are examined, and the problem of optimizing over the set of approximate solutions is addressed. This research was supported by the National Science Foundation, Grant DMS-0425768, and by the Automotive Research Center, a US Army TACOM Center of Excellence for Modeling and Simulation of Ground Vehicles at the University of Michigan     

MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS

In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.     

Multiple criteria decision problems with fuzzy domination structures

The concepts of domination structures and nondominated solutions in multiple criteria decision problems, which were introduced by Yu, enable us to tackle general situations in which there exists information concerning the decision maker's preferences.In many of the multiple criteria decision problems the underlying domination structures are not known precisely but only fuzzily determined. Yu primarily works with the case where the domination structure at each point is a convex cone. As a result, there exists a sharp borderline dividing all solutions into nondominated solutions and the others.This paper fuzzifies the concepts of domination structures and nondominated solutions to allow them to be applied to a larger class of the multiple criteria decision problems mentioned above. Introducing the concepts of fuzzy convex cones and fuzzy polar cones, it is shown how some of the main results obtained by Yu are extended.     

EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION

In this paper, the boundary value problems of p-Laplacian functional differential equation are studied. By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.     

Theory of convex cones in multicriteria decision making

We develop the theory of convex polyhedral cones in the objective-function space of a multicriteria decision problem. The convex cones are obtained from the decision-maker's pairwise judgments of decision alternatives and are applicable to any quasiconcave utility function. Therefore, the cones can be used in any progressively articulated solution procedure that employs pairwise comparisons. The cones represent convex sets of solutions that are inferior to known solutions to a multicriteria problem. Therefore, these convex sets can be eliminated from consideration while solving the problem. We develop the underlying theory and a framework for representing knowledge about the decision-maker's preference structure using convex cones. This framework can be adopted in the interactive solution of any multicriteria problem after taking into account the characteristics of the problem and the solution procedure. Our computational experience with different multicriteria problems shows that this approach is both viable and efficient in solving practical problems of moderate size.     

Characterization of Solid Cones

The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the framework of Banach spaces. In particular, the author gives a dual relationship between solid cones and generalized sharp cones. The related known results are improved and extended.     

On Solidness of Polar Cones

We investigate the properties of cones whose polars are solid in different polar topologies. By a standard duality argument, we obtain a number of necessary and sufficient conditions for closed convex cones to be solid in various locally convex spaces. From this, we can deduce easily the extensions of previous related results. Furthermore, we construct a class of closed convex cones in some Banach spaces, which are not solid but whose polars satisfy the angle property. This solves the Han conjecture in the negative.     

具有较高奇性的奇异边值问题的Dirichiet问题

本文讨论一类奇异二阶常微分方程的边值问题，其中非线性项ｆ（ｔ，ｕ）在ｕ＝０处及在ｔ＝０，１处都具有较高的奇性．应用现有的存在性结果无法得出这类方程的解．利用锥上的不动点定理及解的细致先验估计得到了正解的存在性．     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel'skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.