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中文摘要：
本项目旨在研究脉冲微分方程的最新分支- - 脉冲泛函微分方程的解的各种定性性态.并主要研究时标上的脉冲泛函微分方程各种边值问题解的存在性,周期解的存在性,稳定性等。我们将引入一些新的研究方法，即把变分法和临界点理论中的相关结果推广到时标上的分析上，然后用来研究边值问题。这样便把脉冲泛函微分方程及其离散化形式- - 脉冲泛函差分方程的相应定性性态统一起来进行研究.揭示脉冲泛函微分方程解的一些新的定性现象，并应用新发展起来的相关理论和方法，研究物理、生物、工程技术及经济学中提出来的脉冲泛函微分（差分）方程模型。为有广泛应用前景的模型提供系统的分析方法，这具有重要的理论和实用价值。
英文摘要：
Impulsive equation；Bundary value problem；Stability；Theory of critical points；Time scale
结论摘要：
本项目旨在研究脉冲泛函微分方程解的各种定性性态。并主要研究时标上的脉冲泛函微分方程各种边值问题解的存在性,周期解的存在性及稳定性等，并应用新发展起来的相关理论和方法，研究物理、生物、工程技术及经济学中提出来的脉冲泛函微分方程模型。本项目按计划完成了预定的研究目标。通过本项目的完成，获得了如下的成果（1）建立了一类Sobolev空间理论，并利用临界点理论在其上研究了二阶Hamilton系统的周期解及几类时标上的脉冲动力方程的边值问题；（2） 利用锥不动点定理,拓扑度理论获得了几类非线性（脉冲）动力方程的积分边值问题解的存在性，多重性; （3） 获得了变时标上的一类非线性中立型动力方程多个周期解的存在性；（4）提出并研究了时标上的几类具不同边值条件的反应扩散系统平衡解的存在性和稳定性；（5） 提出了时标上的概周期函数、一致概周期函数和伪概周期函数等的概念，研究了时标上的概周期函数的基本性质，建立了时标上的概周期动力方程的一些基本理论；（6）应用临界点理论研究并获得了若干重要的非线性(脉冲)微分方程边值问题解的存在性及多解性；（7） 得出了若干具重要意义的生物数学模型、神经网络模型等的周期解、多个周期解的存在性、持久性、概周期解存在性和全局吸引性、Hopf分支及稳定性等的依赖于时滞和脉冲或不依赖于时滞和脉冲等的充分条件；上述研究成果由55篇论文具体体现。
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期刊论文
Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Bounda
The existence of nonzero almost periodic solution for Cohen-Grossberg neural networks with continuou
Existence and uniqueness of anti-periodic solution for a kind of forced Rayleigh equation with state
Existence and Global Exponential Stability of Equilibrium Solution to Reaction-Diffusion Recurrent N
Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parame
Anti-periodic solutions for a class of fourth-order nonlinear differential equations with variable c
THREE POSITIVE PERIODIC SOLUTIONS FOR DYNAMIC EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT AND IMPULSE
Solvability of boundary value problems with Riemann-Stieltjes Delta-integral conditions for second-o
On the existence and stability of a unique almost periodic sequence solution in discrete predator-pr
Multiple Positive Solutions for Second-Order p-Laplacian Dynamic Equations with Integral Boundary Co
MULTIPLE POSITIVE PERIODIC SOLUTIONS TO m-LAYER PERIODIC LOTKA-VOLTERRA NETWORK-LIKE MULTIDIRECTIONA
Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effect
Multiple positive periodic solutions for a non-autonomous stage-structured predatory-prey system wit
PERIODIC SOLUTIONS FOR A CLASS OF FUZZY BAM NEURAL NETWORKS WITH DISTRIBUTED DELAYS AND VARIABLE COE
EXISTENCE OF THREE POSITIVE PERIODIC SOLUTIONS FOR DIFFERENTIAL SYSTEMS WITH FEEDBACK CONTROLS ON TI
Three periodic solutions for a class of higher-dimensional functional differential equations with im
Existence of 2(n) Positive Periodic Solutions to n-Species Nonautonomous Food Chains with Harvesting
2(n) Positive Periodic Solutions to n Species Non-Autonomous Lotka-Volterra Unidirectional Food Chai
Existence and Stability of Antiperiodic Solution for a Class of Generalized Neural Networks with Imp
Permanence and almost periodic sequence solution for a discrete delay logistic equation with feedbac
Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scale
Robust stability of delayed reaction-diffusion recurrent neural networks with Dirichlet boundary con
Permanence of a discrete n-species cooperation system with time-varying delays and feedback controls
Existence and Multiplicity of Solutions to a Boundary Value Problem for Impulsive Differential Equat
Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural network
PERMANENCE FOR A COMPETITION AND COOPERATION MODEL OF ENTERPRISE CLUSTER WITH DELAYS AND FEEDBACK CO
Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harves
Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed d
Multiple positive solutions for first-order impulsive integral boundary value problems on time scale
Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time s
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