关于微分包含的周期解及其应用

研究了一类发展包含的周期问题,其结果应用于建立一类半线性微分包含周期解的存在性定理．给出了半线性微分包含端点解的存在性定理和强松驰定理,并且应用于周期反馈控制系统．     

带有非局部条件积分微分包含的可控性

研究了一类带有非局部条件积分微分包含的可控性,利用Kakutani不动点定理和Schauder不动点定理,我们给出了凸和非凸两种情形可控性的充分条件.     

集值映象不动点指数对微分包含与积分包含多解问题的应用

为获得一类微分包含与积分包含的多解存在性定理，我们应用集值映象不动点指数理论把著名的Ａｍａｎｎ三解定理等多解定理推广到集值映象，我们还用例子说明了所得结果．     

具非凸右端项泛函微分包含的周期解

In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.     

Banach空间中微分包含的解

利用不动点方法,证明了Banach-空间中右端项不连续的微分包含解的存在性.     

Banach空间中混合型微分─积分包含解的存在性

研究可分Ｂａｎａｃｈ空间中一类混合型的微分－积分包含，证明了解的存在性，其单值情形改进和推广了文［１～３］中关于混合型微分－积分方程的若干存在性结果．     

Banach空间中混合型微分—积分包含解的存在性

研究可分Banach空间中一类混合型的微分—积分包含，证明了解的存在性，其单值情形改进和推广了[1～3]中关于混合型微分—积分方程的若干存在性结果。     

一类延迟积分方程的渐近概周期解

积分方程解的性态是积分理论中一个重要而又基本的问题.其中关于方程的周期解、概周期型解的存在性问题更是具有重要的理论意义和应用价值.已有文献中,有的延迟是常数,而有的延迟虽为函数,但对延迟做了是概周期函数的假设.本文在某些延迟积分方程的概周期解的存在性的基础上,并利用渐近概周期函数的定义和不动点理论,讨论了一类延迟是渐近概周期函数的积分方程的渐近概周期解的存在性.     

Periodic Solutions for Functional Differential Inclusion with Nonconvex Right Hand Sides

In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.     

On Periodic Solutions of a Class of Differential Equation with Periodic Coefficients

51.IntroductionandtheLemmas.Thefollowingequationy'=f(t,y)=A(t)y" B(t)y C(t)(m22,meN)(l.1)(WhereA(t),B(t)andC(t)areallcontinuousT-periodicfunctions,TXO)isencounteredinseveralappliedareas,sincethisequationplaysanimportantroleinthestudiesofnonlinearos-cillation,fluidmechanicsandthequalitativetheoryofordinarydifferentialequation.Whenm=2,(1.1)isthefamousRiccatiEqation.In1979,ProfessorQinYuanxunansweredthequestionthatunderwhatconditionsRiccatiEquationwithperiodiccoefficientshasthecontinu-ous…     

Existence of Time Periodic Solutions to Boundary Value Problem of One-dimensional Semilinear Viscoelastic Dynamic Equation with Memory

In this paper, we prove the existence of time-periodic solutions to the boundary value problem of semilinear one-dimensional dynamical equation for viscodastic materials.     

随机二阶多值周期问题解的存在性

本文研究了随机二阶多值周期问题解的存在性,在非常一般的假定下建立了凸和非凸问题解的存在性定理,并给出了在随机周期反馈控制系统中的应用．     

Existence of Periodic Solutions for Differential Inclusions

§ 0 .Introduction　 During the past decades,periodic optimal control problems have been paidconsiderable attention;see,for example [1 ]— [9] and the references therein. In orderto deal with such periodic optimal control problems,one often considers the existence ofperiodic solutions for the nonlinear differential systemx′=f(t,x,u)　′=ddt ,where x is the real state n-vector attime t∈ R and u is the control parameter m-vector attime tvarying in some compactsetΩ of Rm,and hence the function…     

周期系数Ricatti方程之周期解

本文利用Brouwer不动定理，研究了Ricatti方程的周期解的存在性。     

一类具周期系数的Riccati型方程的周期解

给出 Riccati型方程x=A( t) x2 m+B( t) x2 k- 1 +C( t)( A( t) ,B( t) ,C( t)是周期为 T的连续函数 ,m,k∈ N且 m≥ k)无周期解及存在周期解的充分条件 .     

高维电报方程的对称周期解

讨论n维电报方程的对称周期解．利用Schauder不动点定理，在非共振条件下给出了一个存在性定理．