一类脉冲型平稳最佳随机控制之研究

本文研究了一类平稳的脉冲控制模型，不仅证明了最佳脉冲控制的存在性而且构造出一个最佳控制．     

Banach空间脉冲Fredholm型积分方程的多解存在性

本文利用Ｋｕｒａｔｏｗｓｋｉ非紧性测芳和不动点理论讨论了Ｂａｎａｃｈ空间脉冲Ｆｒｅｄｈｏｌｍ型积分的多解存在性，并应用于脉冲积分方程组。     

一类脉冲微分系统的有界变差解

在比文[6]更弱的条件下讨论了固定时刻脉冲微分系统与Kurzweil广义常微分方程的关系，并建立了这类脉冲微分系统有界变差解的局部存在性和唯一性定理．     

具有非局部对流一类反应扩散方程脉冲解存在性

该文讨论具有非局部对流的一类反应扩散方程的脉冲解的存在性借助于方程的某种对称性，利用三维空间中追赶法技巧及拓扑方法，当参数ε在一定范围内，证明了方程的脉冲解存在性．最后给出波速Ｃ与人口速率和出生及死亡的动力学过程的相互关系．     

Banach空间非线性脉冲Volterra型积分方程和积分-微分方程的可解性

本文在较宽松的条件下,研究了Banach空间非线性脉冲Volterra型积分方 程和脉冲积分一微分方程解的存在性,建立了新的存在性定理,本质上改进了某些已 知的结果.     

滞后型脉冲泛函微分方程周期解的存在性

本文借助Mawhin重合度理论中的延拓定理和广义常微分方程周期解的存在性,在滞后型脉冲泛函微分方程与广义常微分方程存在等价关系的条件下,建立了滞后型脉冲泛函微分方程周期解的存在性定理.     

非局部条件下的脉冲中立型泛函微分方程

利用Sadovskii不动点定理研究了一类脉冲中立型泛函微分方程，证明了适度解的存在性．最后，给出了上述问题在偏微分方程方面的一个应用．     

中立型脉冲微分方程正解的存在性

本文利用Banach压缩映射原理，讨论了中立型时滞脉冲微分方程正解的存在性。     

线性算子双半群及在间断和脉冲微分方程中的应用(英)

研究抽象Ｂａｎａｃｈ空间中线性微微分方程的可解性,利用算子双半群方法,讨论了在确定时间跳跃或脉冲的线性微分方程解的存在性,表明在一定条件下间断或脉冲方程的解存在唯一．     

带脉冲的EmdenFowler方程次线性奇异边值问题的正解

该文讨论了带脉冲的Emden Fowler方程次线性奇异Dirichlet边值问题,利用上下解方法得到了该类问题正解存在的充分必要条件. 在脉冲的影响下得到了多解的存在性结果。     

Existence conditions for non-safe loads in masonry-like bodies

We study the existence of minimizers for a class of noncoercive functionals, representing the strain energy of masonry-like bodies subject to loads that are not “safe” with respect to certain existence conditions estblished in the literature. Some more general sufficient conditions for existence are proved, and two simple noncoercive examples are discussed making use of these conditions.     

Periodic solutions of abstract functional differential equations with state‐dependent delay

In this paper, we are concerned with the existence of solutions of systems determined by abstract functional differential equations with infinite and state‐dependent delay. We establish the existence of mild solutions and the existence of periodic solutions. Our results are based on local Lipschitz conditions of the involved functions. We apply our results to study the existence of periodic solutions of a partial differential equation with infinite and state‐dependent delay. Copyright © 2016 John Wiley & Sons, Ltd.     

From Scalar to Vector Equilibrium Problems in the Quasimonotone Case

In a unified approach, existence results for quasimonotone vector equilibrium problems and quasimonotone (multivalued) vector variational inequality problems are derived from an existence result for a scalar equilibrium problem involving two (rather than one) quasimonotone bifunctions. The results in the vector case are not only obtained in a new way, but they are also stronger versions of earlier existence results.     

On the Existence of Solutions of Quasi-equilibrium Problems with Constraints

The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of some vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the existence of solutions of quasi-optimization problems with constraints.     

两类分段对称系统周期解的存在性

本文研究了两类分段对称系统周期解的存在性,得到了系统相应的周期解存在的充分条件．作为应用,证明了一类具有分段对称性的时滞微分方程的周期解的存在性,推广了现有的相关结果．     

随机微分—积分方程解的存在唯一性

本文讨论Ｈｉｌｅｒｔ空间中非线性随机微分－积分方程解的存在性,唯一性,在我们所 一组条件下,得到了解的局部存在唯一性的结果。     

含参数泛函微分方程概周期正解的存在性

研究了一类含参数泛函微分方程概周期正解的存在性问题.结合有界性及渐近概周期性获得了系统存在概周期正解的几组充分条件,并将结果应用于几类种群动力学模型,分别获得了系统在概周期环境下存在概周期解的一组充分条件.     

Non-existence and existence of localized solitary waves for the two-dimensional long-wave–short-wave interaction equations

In this study, we establish the non-existence and existence results for the localized solitary waves of the two-dimensional long-wave–short-wave interaction equations. Both the non-existence and existence results are based on Pohozaev-type identities. We prove the existence of solitary waves by showing that the solitary waves are the minimizers of an associated variational problem.     

Existence of Optimal Controls in the Absence of Cesari-Type Conditions forSemilinear Elliptic and Parabolic Systems

Some new results on the existence of optimal controls are established for control systems governed by semilinear elliptic or parabolic equations. No Cesari type conditions are assumed. By proving existence theorems and analyzing the Pontryagin maximum principle for optimal relaxed state-control pairs for the corresponding relaxed problems, existence theorems of classical optimal pairs for the original problem are established. To treat the case of a noncompact control set, relaxed controls defined by finitely additive measures are used.     

BANACH空间中二阶脉冲积分-微分方程初值问题的解

在较弱的条件下,我们研究了Banach空间中二阶脉冲积分-微分方程初值问题解的存在性,建立了解的存在定理,本质地改进了郭大钧的相关结果．同时,利用非紧性测度还给出了存在最大最小解的一个充分条件．