具有连续变量的非线性偏差分方程的振动性

This paper is concerned with the oscillation of nonlinear partial difference equa- tions with continuous variables and the corresponding dual equations.Several sufficient conditions are obtained for the oscillation of these equations.     

具连续变量的三阶非线性中立型差分方程有界解的振动性

研究一类具有连续变量的三阶多时滞中立型非线性差分方程,获得该类方程有界解振动的充分条件.     

Continuous dependence on the geometry and on the initial time for a class of parabolic problems I

In this paper, we investigate the continuous dependence on the geometry and the initial time for solutions u( x , t) of a class of nonlinear parabolic initial‐boundary value problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Analytical solution for general nonlinear continuous systems in a complex form

In this paper, the method of multiple scales is used to study free vibrations and primary resonances of geometrically nonlinear spatial continuous systems with general quadratic and cubic nonlinear operators in a complex form. It is found that in the free vibrations of general continuous systems in a complex form, both forward and backward modes are excited. This situation is in contrast to the primary resonances in which only forward modes are excited. Consequently, one may determine the form of solution before applying the multiple scales method to the equation. This analysis is applicable to general continuous systems with gyroscopic and Coriolis effects and includes many nonlinear problems as a special case. As an example of application of this general solution, free vibrations and primary resonances of a simply supported rotating shaft with stretching nonlinearity are considered.     

一类具连续分布滞量的偶数阶非线性中立型方程的振动定理

研究一类具有连续分布滞量的偶数阶非线性中立型泛函微分方程解的振动性,得到了该类方程的若干新的振动准则.所得结果推广和包含了已知的一些结论.     

一类具连续分布滞量的非线性中立型偏微分方程解的振动性

In this paper,some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet's boundary value conditions.     

以函数为参量的间歇发酵非线性动力系统及其辨识

建立以连续分段线性函数为参量的间歇发酵非线性动力系统,证明该动力系统的主要性质及解的存在性.以实验数据拟合得到的光滑曲线为依据,提出了连续分段线性函数为优化变量的辨识模型,论述可辨识性.依状态变量与辨识函数的相关性,构造求解辨识模型的优化算法,并给出优化算法的收敛性分析及数值结果.     

具连续变量的非线性时滞差分方程的振动性

本文研究了一类具有连续变量的非线性时滞差分方程的振动性,给出了该类方程振动的几个充分条件。     

具连续分布滞量的偶数阶非线性中立型方程的振动准则

研究一类具连续分布滞量的偶数阶非线性中立型泛函微分方程解的振动性,利用数学分析方法和技巧与方程各阶导数的符号关系,建立了该类方程的若干新的振动准则,并通过实例加以阐明.     

一个具有内部物质对流的两项连铸Stefan问题

考虑了一个具有内部物质对流和非线性边界热交换的多维连铸Stefan问题,并得到了这个问题整体弱解的存在性、唯一性和对初边界条件的连续依赖性。本项工作改进和推广了J.F.Fodri-gues＆F.Yi的结果,放宽了他们对内部流和边界条件的一些不太符合实际的限制。     

Oscillation of nonlinear impulsive partial difference equations with continuous variables

By employing a difference inequality without impulses, we establish several sufficient conditions for the oscillation of solutions of a class of nonlinear impulsive partial difference equations with continuous variables.     

A note on the dependence on parameters for a nonlinear system via monotonicity theory

Using monotonicity theory, we investigate the continuous dependence on parameters for the discrete BVPs, which can be written in a form of a nonlinear system.     

Global analysis of continuous analogues of the Levenberg-Marquardt and Newton-Raphson methods for solving nonlinear equations

Summary Global analyses are given to continuous analogues of the Levenberg-Marquardt methoddx/dt=−(J ^t(x)J(x)+δI)⁻¹J^t(x)g(x), and the Newton-Raphson-Ben-Israel methoddx/dt=−J ⁺(x)g(x), for solving an over- and under-determined systemg(x)=0 of nonlinear equations. The characteristics of both methods are compared. Erros in some literature which dealt with related continous analogue methods are pointed out. The Institute of Statistical Mathematics     

基于输出反馈的一类大型互联Holder非线性系统的全局实际镇定

本文研究基于输出反馈的一类大型互联Holder连续非线性系统的全局实际镇定问题.通过构造每个子系统的状态观测器,并对观测器的状态作线性变换,得到分散输出反馈控制器.当输出反馈控制律作用于该系统时,闭环系统是全局实际稳定的.     

DYNAMICS OF A NONLINEAR NON-AUTONOMOUS n-PATCHES PREDATOR-PREY DISPERSION-DELAY MODEL

In this paper,a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied,where all parameters are time-dependent.In this system consisting of n-patches the prey species can disperse among n-patches,but the predator species is confined to one patch and cannot disperse.It is proved that the system is uniformly persistent under any dispersion rate effect.Furthermore,some sufficient conditions are established for the existence of a unique almost periodic solution of the system.The example shows that the criteria in the paper are new,general and easily verifiable.     

Semilinear evolution equations with nonlinear constraints and applications

This paper deals with a general class of evolution problems for semilinear equations coupled with nonlinear constraints. Those constraints may contain compositions of nonlinear operators and unbounded linear operators, and hence the associated operators are not necessarily formulated in the form of continuous perturbations of linear operators. Accordingly, a family of equivalent norms is introduced to discuss 'quasidissipativity' in a local sense of the operators and a generation theory for nonlinear semigroups is employed to construct solution operators on bounded sets. It is a feature of our treatment that the resultant solution operators are obtained as nonlinear semigroups on the whole space which are not 'quasicontractive' but locally equi-Lipschitz continuous.     

The existence of strong solution for a class of fully nonlinear equation

This article mainly investigates the existence of global strong solution of a class of fully nonlinear evolution equation and the strong solution of its steady-state equation. By using the T-compulsorily weakly continuous operator theory, the existence of the global strong solution of the fully nonlinear evolution equation is obtained. In addition, based on the acute angle principle, the W^2,p-strong solution for the corresponding stationary equation is also derived.     

On the well‐posedness of a Volterra equation with applications in the Navier‐Stokes problem

This paper is dedicated to the study of a family of nonlinear Volterra equations coming from the theory of viscoelasticity. We analyze the existence of local mild solutions to the problem and their possible continuation to a maximal interval of existence. We also consider the problem of continuous dependence with respect to initial data.     

具连续分布滞量的二阶中立型方程的振动性定理

利用直接分析方法研究一类具有连续分布滞量的二阶非线性中立型方程解的性质，获得了类具连续分布滞量的二阶非线性中立型泛函微分方程所有解振动的若干充分条件．     

非线性时变广义分布参数系统的适定性问题

本文的主要目的是讨论非线性时变广义分布参数系统的适定性问题.首先,在Banach空间中引入由连续(可能是非线性的)算子引导的非线性广义发展算子,该非线性广义发展算子是广义发展算子的推广,并研究非线性广义发展算子的性质;然后,应用非线性广义发展算子讨论非线性时变广义分布参数系统的适定性问题,并给出解的构造性表达式.