Exploring multiple equilibria for symmetric 2×2 CES/LES pure exchange economies

This paper explores the existence of 3 equilibria for symmetric 2-individual 2-good CES/LES pure exchange economies. For certain parameterizations in the economies, we show analytically that there are no more than 3 equilibria. We generalize our analytical results of existence of 3 equilibria for a wide range of parameterizations. Then we provide examples of 3 equilibria and parameter zones of 3 equilibria for CES and CES/LES economies.     

离散无穷时期不完全资产市场随机平衡

Abstract. This paper examines the existence of general equilibrium in a discrete time economywith the infinite horizon incomplete markets. There is a single good at each node in the eventtree. The existence of general equilibrium for the infinite horizon economy is proved by takinglimit of equilibria in truncated economies in which trade stops at a sequence of dates.     

ON EQUILIBRIA AND PERIODIC ORBITS OF COOPERATIVE SYSTEMS IN R~3

In the paper we present new criteria for existence of equilibria and periodic orbits for 3-dimensional systems which are cooperative. Particular attention is given to the relations of equilibria, cycle K and stable manifold of K. Meanwhile, the results of Hirsch [1, Theorem 9] and Jiang [2] are improved.     

QUALITATIVE ANALYSIS FOR A MATHEMATICAL MODEL OF AIDS

In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.     

Mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes

Considering that HBV belongs to the DNA virus family and is hepatotropic, we model the HBV DNA-containing capsids as a compartment. In this paper, a delayed HBV infection model is established, where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced. According to some preliminaries, including well-posedness, basic reproduction number and existence of two equilibria, we obtain the threshold dynamics for the model. We illus...     

THE LIMIT CYCLES AND HOPF BIFURCATION OF A CLASS OF SIMPLIFIED HOLLING TYPE-IV PREDATOR-PREY SYSTEM WITH LINEAR STATE FEEDBACK

In this paper, a class of simplified Type-IV predator-prey system with linear state feedback is investigated. We prove the boundedness of the positive solutions to this system, and analyze the quality of the equilibria and the existence of limit cycles of the system surrounding the positive equilibra. By Hopf bifurcation theory, the result of having two limit cycles to the system is obtained.     

STRONG SOLUTIONS FOR THE INCOMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE

In this article, we are concerned with the strong solutions for the incompressible fluid models of Korteweg type in a bounded domain Ω R3. We prove the existence and uniqueness of local strong solutions to the initial boundary value problem. We point out that in this article we allow the existence of initial vacuum provided initial data satisfy a compatibility condition.     

HOPF BIFURCATION ANALYSIS OF A 3D CHAOTIC SYSTEM

In this paper,a 3D chaotic system with multi-parameters is introduced. The dynamical systems of the original ADVP circuit and the modified ADVP model are regarded as special examples to the system.Some basic dynamical behaviors such as the stability of equilibria,the existence of Hopf bifurcation are investigated.We analyse the Hopf bifurcation of the system comprehensively using the first Lyapunov coefficient by precise symbolic computation.As a result,in fact we have studied the further dynamical behaviors.     

Random Attractors of Stochastic Modified Boussinesq Approximation

The Boussinesq approximation is a reasonable model to describe processes in body interior in planetary physics.We refer to[1]and[2]for a derivation of the Boussinesq approximation, and[3]for some related results of existence and uniqueness of solution. Let D=[O,L]~2(L>0).We mainly consider the following stochastic modified Boussinesq approximation in two-dimensional periodic domain D,     

在几乎下半连续的假设下抽象经济的均衡

The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken than that they are lower semi-continuous. Several equilibria existence theorems are proved.     

EXISTENCE OF EXTREME SOLUTION TO FIRST-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficient conditions for the existence of extreme solutions by the upper and lower solutions method coupled with a monotone iterative technique.     

Generalized Inverses and Units in a Unitary Ring

Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of units.As applications,the need for two invertible morphisms used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible morphism,and the existence and...     

巴拿赫空间中半群指数吸引子的存在性

We construct an exponential attractor for semigroup in Banach space by using ω-limit compactness method and provide a new method to prove the existence of an exponential attractor in uniformly convex Banach space. As a simple application, we prove the existence of an exponential attractor for reaction diffusion equations.     

PERIODIC SOLUTION TO A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH A STATEMENT-DEPENDENT DEVIATION VARIABLE

We obtain sufficient conditions for the existence of periodic solution to a class of second order neutral functional differential equation,using continuation theorem of the coincidence degree.     

A COUPLED SYSTEM OF INTEGRAL EQUATIONS IN REFLEXIVE BANACH SPACES

We present an existence theorem for at least one weak solution for a coupled system of integral equations of Volterra type in a reflexive Banach spaces relative to the weak topology.     

Periodic Orbits for Some Systems of Delay Differential Equations

We provide sufficient conditions for the existence of periodic orbits of some systems of delay differential equations with a unique delay. We extend Kaplan-Yorke＇s method for finding periodic orbits from a delay differential equation with several delays to a system of delay differential equations with a unique delay.     

Existence of Solution for a Coupled System of Fractional Integro-Differential Equations on an Unbounded Domain

We present the existence of solution for a coupled system of fractional integro-differential equations. The differential operator is taken in the Caputo fractional sense. We combine the diagonalization method with Arzela-Ascoli theorem to show a fixed point theorem of Schauder.     

Implicit Complementarity Problems in Banach Spaces

We utilize the method of multivalued fixed point in this paper to prove the existence theorems of solutions for some implicit complementarity problems in Banach spaces.     

The Solution to Impulse Boundary Value Problem for a Class of Nonlinear Fractional Functional Differential Equations

In this paper, we investigate the existence of solution for a class of impulse boundary value problem of nonlineax fractional functional differential equation of mixed type. We obtain the existence results of solution by applying some well-known fixed point theorems. An examule is given to illustrate the effectiveness of our result.     

Mather theory for piecewise smooth Lagrangian systems

We establish the Mather theory for a type of piecewise smooth and positive definite Lagrangian systems.It models a mechanical system subject to external impulsive forcing.We show the existence of the minimal measure and the Lipschitz property of Aubry set.In addition,the weak KAM solution to this kind of piecewise smooth Lagrangian is also established.