Oscillation of Nonlinear Partial Difference Equations with Continuous Variables

This paper is concerned with the oscillation of nonlinear partial difference equations with continuous variables and the corresponding dual equations. Several sufficientconditions are obtained for the oscillation of these equations.

BOUNDS FOR SOLUTIONS OF A THREE-POINT PARTIAL DIFFERENCE EQUATION

This paper is concerned with a class of partial difference equations with variable coefficients. Explicit growth bounds are found for their solutions. These bounds provide information on the existence of exponentially bounded solutions.

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF HYPERBOLIC AND ELLIPTIC TYPE PARTIAL DIFFERENCE EQUATIONS

This paper is concerned with hyperbolic type delay partial difference equation and elliptic type equation where a, b,p, qi are real numbers, hi and h are nonnegative integers, a, b,p ≠ 0 and not all of qi are zero for 1 ≤ i ≤ u. Sufficient and necessary conditions for all solutions of the equation mentioned above to be oscillatory are obtained.

Admissible Solutions of Systems of Complex Partial Difference Equations on C^n

In a recent papers,some authors applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. We will mainly investigate Malmquist theorem of a type of systems of complex partial difference equations on Cn,improvements and extensions of such results are presented in this paper.

EXPONENTIAL STABILITY OF A PARTIAL DIFFERENCE EQUATION WITH NONLINEAR PERTURBATION

Stability criteria are established for partial difference equations with nonlinear pertubations.

BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED K-HOLOMORPHIC FUNCTIONS IN C^(2)

In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.

Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations

This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.

SOME PROBLEMS OF FRACTIONAL PARTIAL DIFFERENCE DIFFUSION EQUATIONS

This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method.

ON SOME DISCRETE INEQUALITIES USEFUL IN THE THEORY OF CERTAINPARTIAL FINITE DIFFERENCE EQUATIONS

The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analysis used in the proof is elementary and the results established provide new estimates for these types of inequalities.AMS (MOS) Subject Classification (1991 ): Primary 26D15.

Classification of discrete equations linearizable by point transformation on a square lattice

We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a MSbious transformation.

Optimal linear estimator for discrete-time systems with random delays

In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into the one with both multiplicative noises and constant delays. Then, an estimator which includes the cases of smoothing and filter- ing, is derived via the projection formula, and the solution is given in terms of a partial difference Riccati equation with boundary conditions. A predictor for such systems is also presented based on the proposed filter and smoother. The ob- tained estimators have the same dimension as the original state. Conditions for existence, uniqueness, and stability of the steady-state optimal estimators are studied for time-invariant cases. In this case, the obtained estimators are very easy to implement and all calculations can be performed off line, leading to a linear time-invariant estimator.

A REMARK FOR “ASYMPTOTIC BEHAVIOR OF DELAY 2-D DISCRETE LOGISTIC SYSTEMS”

In this remark,we shall show some counter examples for the main results of the recent paper 'Asymptotic Behavior of Delay 2-D Discrete Logistic Systems' (IEEE Trans.Circuits Systems,49(2002),1677-1682.)