ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an appplication, we utilize the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equations. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of.     

EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L^2-SPACES

By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta (1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L^2 (Ω) are studied. The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen‘s previous papers. Especially,some new techniques are used in this paper.     

ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE

By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.     

与 p-Laplacian 算子相关的非线性Neumann边值问题解的存在性

Using perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present the abstract results on the existence of solutions of one kind nonlinear Neumann boundary value problems related to p-Laplacian operator. The equation discussed in this paper and the method used here extend and complement some of the previous work.     

偏微分方程的吸引子

Abstract. In this paper the reaction-diffusion systems and the damped wave systems with non-linear terms of gradient form are studied ,and the conditions for making them to be gradient sys-tems are given. So the structure of attractors is clear and simple in some sense by the known re-sult. Some examples are given. Also the reaction-diffusion systems with general nonlinear termsare discussed.     

Generalized system for strongly <Emphasis Type="Italic">g-r</Emphasis>-pseudomonotonic nonlinear variational inequalities in Hilbert spaces

The approximation solvability of a generalized system for strongly g-r- pseudomonotonic nonlinear variational inequalities in Hilbert spaces is studied based on the convergence of the projection method. The results presented in this paper improve, generalize and unify some recent results in the literature.     

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

The initial value problem of a nonlinear fractional differential equation is discussed in this paper. Using the nonlinear alternative of Leray-Schauder type and the contraction mapping principle,we obtain the existence and uniqueness of solutions to the fractional differential equation,which extend some results of the previous papers.     

ASYMPTOTIC STABILITY OF A CLASS OF NONLINEAR NEUTRAL-TYPE SYSTEMS

By Lyapunov functional method, sufficient conditions for the asymptotic stability of a class of neutral-type systems are discussed in this paper. This work extends some results on the stability of neutral-type systems in the previous papers. Several numerical examples are listed in the end of this paper to confirm our results.     

赋范空间中φ-伪压缩型映象的收敛定理

in this paper,by virtue of an inequality and some analysis techniques,we prove some convergence theorems on the iterative process for nonlinear mappings of Φ-pseudo contractive type in normed linear spaces,which extend and improve the corresponding results obtained by others recently.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH DELAY

Using a fixed point method, in this paper we discuss the existence and uniqueness of positive solutions to a class system of nonlinear fractional differential equations with delay and obtain some new results.     

A Method for Constructing Traveling Wave Solutions to Nonlinear Evolution Equations

In this paper, an analytical method is proposed to construct explicitly exact and approximate solutions for nonlinear evolution equations. By using this method, some new traveling wave solutions of the Kuramoto-Sivashinsky equation and the Benny equation are obtained explicitly. These solutions include solitary wave solutions, singular traveling wave solutions and periodical wave solutions. These results indicate that in some cases our analytical approach is an effective method to obtain traveling solitary wave solutions of various nonlinear evolution equations. It can also be applied to some related nonlinear dynamical systems.     

非线性系统的线性对称结构

非线性系统的线性对称结构洪奕光，程代展（中国科学院系统科学研究所，北京１０００８０）１９９１年１２月２０日收到．１９９３年９月１６日收到压缩稿，一、引言近年来，人们对非线性控制系统对称性问题的研究很感兴趣．这主要是因为现实世界存在着大量的对称现象，而...     

Adaptive synchronization to a general non-autonomous chaotic system and its applications

In this paper, new adaptive synchronous criteria for a general class of n-dimensional non-autonomous chaotic systems with linear and nonlinear feedback controllers are derived. By suitable separation between linear and nonlinear terms of the chaotic system, the phenomenon of stable chaotic synchronization can be achieved using an appropriate adaptive controller of feedback signals. This method can also be generalized to a form for chaotic synchronization or hyper-chaotic synchronization. Based on stability theory on non-autonomous chaotic systems, some simple yet less conservative criteria for global asymptotic synchronization of the autonomous and non-autonomous chaotic systems are derived analytically. Furthermore, the results are applied to some typical chaotic systems such as the Duffing oscillators and the unified chaotic systems, and the numerical simulations are given to verify and also visualize the theoretical results.     

A novel approach to exponential stability of nonlinear systems with time-varying delays

In this paper, the stability of nonlinear systems with time-varying delays is investigated by means of the concepts of generalized Dahlquist constant, generalized relative Dahlquist constant and relative minimal Lipschitz constant. In detail, two sufficient conditions are derived for the exponential stability of nonlinear systems with time-varying delays and the exponential decay of the solutions is also estimated. Compared with some existing results, our stability conditions are less conservative. Some examples are given to illustrate the effectiveness of the obtained results.     

一类具有分离变量的非线性离散系统的镇定控制器

在控制理论和控制工程中，镇定控制器的设计是一个经典问题。许多有关这个问题的结论一般都是针对线性系统。对于非线性系统，很少见到有构造性结果能用于控制工程中。本针对一类广泛的非线性控制系统，我们构造了一些控制器，这些判据在工程实际问题中将具有一定的指导意义。     

Exact solutions of some nonlinear systems of partial differential equations by using the first integral method

In recent years, many approaches have been utilized for finding the exact solutions of nonlinear systems of partial differential equations. In this paper, the first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including, KdV, Kaup–Boussinesq and Wu–Zhang systems, analytically. By means of this method, some exact solutions for these systems of equations are formally obtained. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.     

非线性灰色离散系统零解的稳定性

本文用区间矩阵和Ｌｙａｐｕｎｏｖ第二方法讨论了具有非线性扰动项的灰色离散系统的稳定性，得到了若干稳定性的代数判据，这些结果将文（５）的主要结果由线性推广到了非线性，并给出了实现的例子。     

Existence of analytic solutions to analytic nonlinear q-difference equations

In this paper, some analytic approaches are formulated for the existence of analytic solutions of analytic nonlinear difference equations. From the point of view of dynamical systems, analytic solutions of such kinds of equations can be generally expressed by formal power series of exponential variables, so we are interested in considering a difference equation as a q-difference equation via a suitable coordinate transformation. After stating analytic results for formal series solutions of nonlinear q-difference equations, we also derive some results for the existence of analytic solutions to autonomous rational difference equations.     

New results on the parametric stability of nonlinear systems

In this paper, we derive some new results on the parametric stability of nonlinear systems. Explicitly, we derive a necessary and sufficient condition for a nonlinear system to be locally parametrically exponentially stable at an equilibrium point. We also derive a necessary condition for the nonlinear system to be locally parametrically asymptotically stable at an equilibrium point. Next, we derive some new results on the parametric stability of discrete-time nonlinear systems. As in the continuous case, we derive a necessary and sufficient condition for a discrete-time nonlinear system to be locally parametrically exponentially stable at an equilibrium point. We also derive a necessary condition for the discrete-time nonlinear system to be locally parametrically asymptotically stable at an equilibrium point. We illustrate our results with some classical examples from the bifurcation theory.     

Homoclinic solutions of discrete nonlinear systems via variational method

Homoclinic solutions arise in various discrete models with variational structure, from discrete nonlinear Schr\"{o}dinger equations to discrete Hamiltonian systems. In recent years, a lot of interesting results on the homoclinic solutions of difference equations have been obtained. In this paper, we review some recent progress by using critical point theory to study the existence and multiplicity results of homoclinic solutions in some discrete nonlinear systems with variational structure.