带有外部输入项的时间周期SIR传染病模型的周期行波解北大核心CSCD

研究了一类带有外部输入项的时间周期SIR传染病模型周期行波解的存在性和不存在性.首先,通过构造辅助系统适当的上下解并定义闭凸锥,将周期行波解的存在性转化为定义在这个闭凸锥上的非单调算子的不动点问题,利用Schauder不动点定理建立辅助系统周期解的存在性,并利用Arzela-Ascoli定理证明了原模型周期行波解的存在性.其次,借助分析技术得到了周期行波解的不存在性.     

广义Davey-Stewartson方程组的整体解及自相似解

本文研究Dalvey-Stewartson方程组的整体解与自相似解的存在性.首先,运用Ba- nach不动点定理得到一个关于解整体存在性的一般性定理,然后把一类特殊的初始值用到该存在性结果上去从而得到自相似解存在的结论.     

Liénard系统的比较定理

研究了Liénard方程的一类新的等价系统解的有界性与周期解的存在性.证明了几个比较定理,使传统Liénard方程等价系统解的有界性和周期解的存在性可用于判定新等价系统解的有界性与周期解的存在性.     

一类时滞微分系统的周期解

研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.     

无界区域中半线性椭圆型方程的渐近解

本文讨论一类无界区域中半线性椭圆型方程渐近解的存在性,包括最大解与最小解的存在性。最后讨论了存在最大解的必要条件,并得到了一个存在最大解的充要条件。     

一类带有扩散与时滞的流行性传染病模型的行波解

讨论了一类带有扩散与时滞的流行性传染病模型的行波解的存在性.首先,将系统的行波解的存在性问题转化为一个二阶常微分方程组的单调解的存在性问题;应用单调方法和不动点方法,进一步地将问题转化为方程组的上下解的构造问题;应用所建立的引理与定理,通过构造适合的上下解,证明了系统单调行波解的存在性.     

带有凹凸非线性项的Klein-Gordon-Maxwell系统解的存在性和多重性

研究一类Klein-Gordon-Maxwell系统解的存在性和多重性.当非线性项是凹凸非线性项时,利用变分方法获得了系统解的存在性和多重性结果,并完善了此系统解的存在性的已有结果.     

Hopfield神经网络概周期解的存在性和全局吸引性

该文研究Ｈｏｐｆｉｅｌｄ神经网络概周期解的存在性和全局吸性,获得了该网络存在唯一概周期解的充分条件和所有解收敛于此概周期解的充分条件。     

一类泛函微分方程半正问题的正周期解

运用Krasnosel’skii不动点理论研究了一类含参泛函微分方程半正问题正周期解的存在性．获得了当参数充分小时正周期解的存在性结果以及半正问题正周期解存在的充分条件．丰富了一阶泛函微分方程解的存在性理论．     

带有非局部扩散项和时空时滞的Kermack-McKendrick传染病模型的行波解

本文主要考虑带有非局部扩散项和反应项的Kermack-Mc Kendrick传染病模型的行波解的存在性问题,得出行波解的存在性不仅与基本再生数有关,还与波速有关.同时,还可以得到行波解的移动速度依赖于个体之间的相互作用以及个体的空间运动.利用Schauder不动点定理得到行波解的存在性,利用Laplace变换的性质得到行波解的不存在性.     

Almost Periodic Solutions of Nonlinear Second Order Differential Equations

We provide existence results for almost periodic solutions of nonlinear second order ordinary differential equations. The results extend existence results for periodic solutions of periodic equations, where the existence of periodic sub and supersolutions implied the existence of periodic solutions.     

System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of the Debreu vector equilibrium problems and the Nash vector equilibrium problems.     

Square of countably compact groups without non-trivial convergent sequences

We show in ZFC that the existence of a countably compact Abelian group without non-trivial convergent sequences implies the existence of a countably compact group whose square is not countably compact.This improves a result obtained by van Douwen in 1980: the existence of a countably compact Boolean group without non-trivial convergent sequences implies the existence of two countably compact groups whose product is not countably compact in ZFC.Hart and van Mill showed in 1991 the existence of a countably compact group whose square is not countably compact under Martin's Axiom for countable posets. We show that the existence of such an example does not depend on some form of Martin's Axiom.     

Variational inclusions problems with applications to Ekeland’s variational principle,fixed point and optimization problems

In this paper, we prove the existence theorems of two types of systems of variational inclusions problem. From these existence results, we establish Ekeland’s variational principle on topological vector space, existence theorems of common fixed point, existence theorems for the semi-infinite problems, mathematical programs with fixed points and equilibrium constraints, and vector mathematical programs with variational inclusions constraints.     

线性增长条件下一类非线性梁方程解的存在性

考察了一类非线性四阶两点边值问题的解的存在性.通过构造适当的Banach空间并且利用积分方程建立了一个存在定理.主要工具是Leray-Schauder非线性抉择.本文表明,如果非线性项在其定义域的某个有界子集上的增长速度是线性的,该问题可能存在解.     

抽象空间中无穷时滞微分方程概自守解的存在性

研究抽象空间中无穷时滞微分方程概自守解的存在性,证明了在正实轴上存在有界解蕴含存在概自守解,并给出了结论在L otka-V o lterra型方程中的应用.我们的结果推广了经典的关于非齐次线性概周期微分方程概周期解存在性的结论.     

On a New Class of Systems of Generalized Quasi-Variational Inequalities

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.     

Traveling waves in delayed lattice dynamical systems with competition interactions

This paper deals with the existence of traveling wave solutions of a class of delayed system of lattice differential equations, which formulates the invasion process when two competitive species are invaders. Employing the comparison principle of competitive systems, a new cross-iteration scheme is given to establish the existence of traveling wave solutions. More precisely, by the cross-iteration, the existence of traveling wave solutions is reduced to the existence of an admissible pair of upper and lower solutions. To illustrate our main results, we prove the existence of traveling wave solutions in two delayed two-species competition systems with spatial discretization. Our results imply that the delay appeared in the interspecific competition terms do not affect the existence of traveling wave solutions.     

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。