凹角型区域椭圆边值问题的自然边界归化

In this paper, the natural boundary reduction for some elliptic boundary value problems with concave angle domains and their natural boundary methods are investigated. The natural integral equations and the Poisson integral formulae are given. The finite element methods of the natural integral equations are discussed in details. The convergences of the approximate solutions and their error estimates are obtained. Finally, some numerical examples are presented to show that our methods are effective.     

Recursive equations for compound distribution with the severity distribution of the mixed type

In this paper, recursive equations are obtained for compound distribution with the number of claims belonging to (a, b)-family and the severity distribution of the mixed type. Numerical methods to solve these equations are presented, and some numerical results are given.     

INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS

Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper.     

ON THE HYPERSPHERICAL HARMONIC METHODTO THREE AND FOUR BODY NUCLEAR PROBLEMS

In this paper, the hyperspherical harmonics used for solving the three and four body problems in nuclear physics are given. The equations of the adiabatic approximation to hyperspherical harmonic method are derived. Some properties of the hypernuclous Heare given as the illustrative example of the application of this method.     

Block monotone iterative algorithms for variational inequalities with nonlinear operators

Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.     

φ0-STRICT STABILITY OF DELAY DIFFERENCE EQUATIONS WITH VARIATIONAL LYAPUNOV METHOD

In this paper, a new type of stability, namelyφ0-strict stability is extended for the delay difference equations, and by using variational cone-valued Lyapunov-like functions some sufficient conditions for such stability to hold are given.     

非局部抛物型方程解的性质

In this short note, we investigate the properties of positive solutions for some non-local parabolic equations. The conditions on the global existence and blow-up in finite time of solution are given.     

A class of stochastic differential equations with the time average

Stochastic diferential equations with the time average have received increasing attentions in recent years since they can ofer better explanations for some fnancial models.Since the time average is involved in this class of stochastic diferential equations,in this paper,the linear growth condition and the Lipschitz condition are diferent from the classical conditions.Under the special linear growth condition and the special Lipschitz condition,this paper establishes the existence and uniqueness of the solution.By using the Lyapunov function,this paper also establishes the existence and uniqueness under the local Lipschitz condition and gives the p-th moment estimate.Finally,a scalar example is given to illustrate the applications of our results.     

Dynamical understanding of loop soliton solution for several nonlinear wave equations

It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.     

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.