脉冲中立型时滞微分方程的振动性

证明了线性脉冲中立型时滞微分方程解的振动性等价于一类非脉冲中立型时滞微分方程解的振动性,应用这一结果建立了此类线性脉冲中立型微分方程解的振动性的显示判据。     

线性分数阶中立型系统的有限时间稳定

本文研究了一类Caputo分数阶中立型系统.利用分步法,获得了该系统的初值问题的存在唯一性结果,再利用Gronwall不等式,证明了该系统的有限时间稳定性.     

The Fundamental Solution and Its Role in the Optimal Control of Infinite Dimensional Neutral Systems

In this work, we shall consider standard optimal control problems for a class of neutral functional differential equations in Banach spaces. As the basis of a systematic theory of neutral models, the fundamental solution is constructed and a variation of constants formula of mild solutions is established. We introduce a class of neutral resolvents and show that the Laplace transform of the fundamental solution is its neutral resolvent operator. Necessary conditions in terms of the solutions of neutral adjoint systems are established to deal with the fixed time integral convex cost problem of optimality. Based on optimality conditions, the maximum principle for time varying control domain is presented. Finally, the time optimal control problem to a target set is investigated.     

Analysis of the neutral layer offset of bimetal composite plate in the straightening process using boundary element subfield method

In the classical straightening theory, it supposes that the geometric central layer and stress neutral layer are a coincidence. However, there is some offset in fact. This is one of the reasons why straightening force is inaccurate in the straightening process. In this paper, the boundary element subfield method is used to analyze the three-dimension elastic–plastic deformation of a bimetal composite plate in the straightening process. At first, the boundary integral equation of a bimetal composite plate is established by the boundary element subfield method. Then, through analyzing the deformation in the rolled piece straightening, it shows that the geometric central layer does not coincide with the neutral layer. The formula of the neutral layer offset is established and the change law is discussed. At the same time, the influence of the neutral layer offset on the precision of straightening force is researched. From the numerical analysis, it shows that the error of the straightening force reaches to 5% whether considering the neutral layer offset. This demonstrates that the neutral layer offset is one of the important factors to give the straightening force inaccurately. It is ought to consider the neutral layer offset when the model of straightening force is established.     

Pseudo-almost periodic solutions of neutral integral and differential equations with applications

The existence and uniqueness of pseudo-almost periodic solutions to general neutral integral equations with deviations are obtained. For this, pseudo-almost periodic functions in two variables are considered. The results extend the corresponding ones to the convolution type integral equations. They are used to study pseudo-almost periodic solutions of general neutral differential equations and to the so-called scalar neutral logistic equation version.     

Binding of atoms and stability of molecules in hartree and thomas-fermi type theories.

This paper is the fourth of a series devoted to the study of the stability of general molecular systems in Thomas-Fermi or Hartree type models. In the preceding part, we proved the bindingof arbitrary neutral systems for Thomas-Fermi type theories and of planar neutral systems forthe Hartree model. In this part, we manage to get rid of this restriction and thus, prove thebinding and the stability of arbitrary neutral systems for the Hartree model.     

Periodic Solutions of Neutral Functional Differential Equations

Periodic neutral functional differential equations are considered.Sufficient conditions for existence, uniqueness and global attractivityof periodic solutions are established by combining the theoryof monotone semiflows generated by neutral functional differentialequations and Krasnosel'skii's fixed-point theorem. These resultsare applied to a concrete neutral functional differential equationthat can model single-species growth, the spread of epidemics,and the dynamics of capital stocks in a periodic environment.     

On Spectral Method for Volterra Functional Integro-Differential Equations of Neutral Type

The main purpose of this work is to provide a numerical method for the solution of Volterra functional integro-differential equations of neutral type based on a spectral approach. We analyze the convergence properties of the spectral method to approximate smooth solutions of Volterra functional integro-differential equations of neutral type. It is shown that for the neutral integro-differential equations, the spectral methods yield an exponential order of convergence.     

高阶脉冲中立型偏泛函微分方程的强迫振动性

研究一类具高阶Laplace算子的高阶脉冲非线性中立型偏泛函微分方程的强迫振动性,利用Green公式和微分不等式方法将所讨论的脉冲中立型偏微分方程转化为脉冲中立型微分不等式的问题,获得了这类方程在三类不同边值条件下所有解强迫振动的若干充分条件.