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 t...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.展开更多
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 investig...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.展开更多
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 fo...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.展开更多
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...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.展开更多
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 a...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.展开更多
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 discret...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.展开更多
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 ...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.展开更多
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 analys...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.展开更多
This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathemat...This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathematics,control,engineering and so on,and thus has received great attention in the past decades.Different from the previous articles where the operator is applied to present the controller,the main contribution of this paper is to propose the discretisation-then-continuousization method,which is explicit and implementable.The solvability condition of the LQ optimal control problems is given based on a set of differential Riccati equations,and an explicit numerical calculation way of these equations and the design of the optimal controller are provided.展开更多
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 ...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.展开更多
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.)
基金Supported by the NSF of China(60174010)Supported by NSF of Hebei Province(102160)Supported by NS of Education Office in Heibei Province(2004123)
文摘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.
基金Supported by the National Natural Science Foundation of China(No.10471065)the Natural Science Foundation of Guangdong Province(No.04010474)
文摘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.
文摘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.
文摘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.
基金supported by the NSF of Henan Province(222300420397,242300421394)Xie’s research was supported by the NSFC(11571089,11871191).
文摘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.
基金supported by the National Natural Science Foundation of China under Grant Nos.61821004 and 62250056the Natural Science Foundation of Shandong Province under Grant Nos.ZR2021ZD14 and ZR2021JQ24+1 种基金Science and Technology Project of Qingdao West Coast New Area under Grant Nos.2019-32,2020-20,2020-1-4,High-level Talent Team Project of Qingdao West Coast New Area under Grant No.RCTDJC-2019-05Key Research and Development Program of Shandong Province under Grant No.2020CXGC01208.
文摘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.
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China[grant numbers 61821004,62250056]the Natural Science Foundation of Shandong Province[grant numbers ZR2021ZD14,ZR2021JQ24]+2 种基金Science and Technology Project of Qingdao West Coast New Area[grant numbers 2019-32,2020-20,2020-1-4]High-level Talent Team Project of Qingdao West Coast New Area[grant number RCTD-JC-2019-05]Key Research and Development Program of Shandong Province[grant number 2020CXGC01208].
文摘This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathematics,control,engineering and so on,and thus has received great attention in the past decades.Different from the previous articles where the operator is applied to present the controller,the main contribution of this paper is to propose the discretisation-then-continuousization method,which is explicit and implementable.The solvability condition of the LQ optimal control problems is given based on a set of differential Riccati equations,and an explicit numerical calculation way of these equations and the design of the optimal controller are provided.
文摘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.
文摘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.)
