半序Menger PM-空间中广义弱压缩映射的最佳逼近点定理

本文利用三个控制函数给出了半序Menger PM-空间中满足特定条件的广义弱压缩映射的最佳逼近点定理,并给出了最佳逼近点唯一的充分条件.进一步地,还给出了主要结果的一些推论.     

三点粗异宿环分支

本文研究高维系统连接三个鞍点的粗异宿环的分支问题.在一些横截性条件和非扭曲条件下,获得了Γ附近的1-异宿三点环, 1-异宿两点环、 1-同宿环和1-周期轨的存在性,唯一性和不共存性.同时给出了分支曲面和存在域.上述结果被进一步推广到连接l个鞍点的异宿环的情况,其中l≥2.     

Sewing method for weak solutions of second-order hyperbolic equation with variable domains of discontinuous unbounded operators

We prove the existence and uniqueness of global weak solutions on the entire interval for the Cauchy problem for hyperbolic differential-operator equations with time-discontinuous operators that have variable domains and satisfy certain matching conditions at the points of discontinuity. To this end, we develop a method of successive sewing of existing local weak solutions of Cauchy problems on the smoothness intervals of the operators. The sewing method is based on special energy inequalities, which imply the time continuity of local weak solutions in the main space and of their first derivatives in some negative spaces and hence the existence of the corresponding limit values at the points of discontinuity. These values, with regard for the matching conditions, are taken for the initial data on each successive interval.     

Incomplete Inverse Spectral and Nodal Problems for Differential Pencils

We prove uniqueness theorems for so-called half inverse spectral problem (and also for some its modification) for second order differential pencils on a finite interval with Robin boundary conditions. Using the obtained result we show that for unique determination of the pencil it is sufficient to specify the nodal points only on a part of the interval slightly exceeding its half.     

Uniqueness of a cycle with discounting that is optimal with respect to the average time profit

For cyclic processes modeled by periodic motions of a continuous control system on a circle, we prove the uniqueness of a cycle maximizing the average one-period time profit in the case of discounting provided that the minimum and maximum velocities of the system coincide at some points only and the profit density is a differentiable function with a finite number of critical points. The uniqueness theorem is an analog of Arnold’s theorem on the uniqueness of such a cycle in the case when the profit gathered along the cycle is not discounted.     

EXISTENCE OF MILD SOLUTIONS TO NEUTRAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.     

Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

In this paper, we study the bifurcation problems of rough heteroclinic loops connecting three saddle points for a higher-dimensional system. Under some transversal conditions and the nontwisted condition, the existence, uniqueness, and incoexistence of the 1-heteroclinic loop with three or two saddle points, 1-homoclinic orbit and 1-periodic orbit near Γ are obtained. Meanwhile, the bifurcation surfaces and existence regions are also given. Moreover, the above bifurcation results are extended to the case for heteroclinic loop with l saddle points. Received January 4, 2001, Accepted July 3, 2001.     

Inverse Sturm–Liouville problems with the potential known on an interior subinterval

The uniqueness problem of inverse Sturm–Liouville problems with the potential known on an interior subinterval is considered. We prove that the potential on the entire interval and boundary conditions are uniquely determined in terms of the known eigenvalues and some information on the eigenfunctions at some interior point (interior spectral data). Moreover, we also concern with the situation where the potential q is C^2k-smoothness at some given points.     

赋范线性空间中同时远达点的唯一性

1 引言 设X为一实赋范线性空间,给定X中的子集G和有界子集K,令(?)和C分别表示X的所有非空有界子集与相对紧子集的全体,对A∈B,记 若x_(0)∈K满足sup||a-x_(0)||=Fk(A),则称x_(0)是A关于K的同时远达点,A关于K的同时远达点的全体记为Q_(K)(A),即     

ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.     

一类生化系统的数学模型及定性分析

研究了一类非线性生化系统极限环的存在性与唯一稳定性,利用定性分析的方法研究了生化系统轨线的全局结构,给出了极限环存在与稳定的判别条件,改进和推广了已有的结果.     

Neumann-Type Boundary Conditions for Hamilton-Jacobi Equations in Smooth Domains

Neumann or oblique derivative boundary conditions for viscosity solutions of Hamilton-Jacobi equations are considered. As developed by P.L. Lions, such boundary conditions are naturally associated with optimal control problems for which the state equations employ "Skorokhod" or reflection dynamics to ensure that the state remains in a prescribed set, assumed here to have a smooth boundary. We develop connections between the standard formulation of viscosity boundary conditions and an alternative formulation using a naturally occurring discontinuous Hamiltonian which incorporates the reflection dynamics directly. (This avoids the dependence of such equivalence on existence and uniqueness results, which may not be available in some applications.) At points of differentiability, equivalent conditions for the boundary conditions are given in terms of the Hamiltonian and the geometry of the state trajectories using optimal controls.     

Quasi-asymptotic contractions,set-valued dynamic systems,uniqueness of endpoints and generalized pseudodistances in uniform spaces

For set-valued dynamic systems in uniform spaces we introduce the concept of quasi-asymptotic contractions with respect to some generalized pseudodistances, describe a method which we use to establish general conditions guaranteeing the existence and uniqueness of endpoints (stationary points) of these contractions and exhibit conditions such that for each starting point each generalized sequence of iterations (in particular, each dynamic process) converges and the limit is an endpoint. The definition, result, ideas and techniques are new for set-valued dynamic systems in uniform, locally convex and metric spaces and even for single-valued maps.     

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents北大核心CSCD

该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题。首先,由不动点原理,证明了问题解的局部存在性和唯一性。其次,利用上下解方法,给出在齐次Dirichlet边界条件下,问题的解在有限时间发生爆破的充分条件,即变指数大于零且初始值足够大,并对爆破时间的上下界进行了估计。     

The Existence and Behavior of Global Solutions to a Mixed Problem with Acoustic Transmission Conditions for Nonlinear Hyperbolic Equations with Nonlinear Dissipation

A mixed problem with acoustic transmission conditions for nonlinear hyperbolic equations with nonlinear dissipation is considered. The existence, uniqueness, and exponential decay of global solutions to this problem with focusing nonlinear sources are proved Additionally, the existence of global solutions and the solution blow-up in a finite time are proved for the case of defocusing nonlinear sources.     

Buckling of a nonlinear elastic rod

The buckling of a pin-ended slender rod subjected to a horizontal end load is formulated as a nonlinear boundary value problem. The rod material is taken to be governed by constitutive laws which are nonlinear with respect to both bending and compression. The nonlinear boundary value problem is converted to a suitable integral equation to allow the application of bounded operator methods. By treating the integral equation as a bifurcation problem, the branch points (critical values of load) are determined and the existence and form of nontrivial solutions (buckled states) in the neighborhood of the branch points is established. The integral equation also affords a direct attack upon the question of uniqueness of the trivial solution (unbuckled state). It is shown that, under certain conditions on the material properties, only the trivial solution is possible for restricted values of the load. One set of conditions gives uniqueness up to the first branch point.     

Constructing bimatrix games with unique equilibrium points

We construct bimatrix games with prefixed equilibrium points in the mixed extension. The uniqueness conditions are studied and we obtain a wide class of games with unique arbitrary prefixed equilibrium points.     

Problems of determining the temperature and density of heat sources from the initial and final temperatures

Under consideration are the three problems that simulate the process of determining the temperature and density of heat sources from some given initial and final temperatures. In the course of their mathematical formulation, some inverse problems arise for the heat transfer equation in which, together with the solution of the equation, one needs also to find the unknown right-hand side that depends only on the spatial variable. The existence and uniqueness theorems are proved for the solution.     

一类平面多项式系统极限环的存在唯一性

研究一类平面2n 1次多项式微分系统的极限环问题,利用Hopf分枝理论得到了该系统极限环存在性与稳定性的若干充分条件,利用Cherkas和Zheilevych的唯一性定理得到了极限环唯一性的若干充分条件.     

Uniqueness and counterexamples in some inverse source problems

Uniqueness of a solution is investigated for some inverse source problems arising in linear parabolic equations. We prove new uniqueness results formulated in Theorems 3.1 and 3.2. We also show optimality of the conditions under which uniqueness holds by explicitly constructing counterexamples, that is by constructing more than one solution in the case when the conditions for uniqueness are violated.