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1.
本文研究了无限滞后测度泛函微分方程的平均化.利用广义常微分方程的平均化方法,在无限滞后测度泛函微分方程可以转化为广义常微分方程的基础上,获得了这类方程的周期和非周期平均化定理,推广了一些相关的结果.  相似文献   

2.
本文利用广义常微分方程的平均化定理,建立脉冲滞后泛函微分方程周期及非周期的平均化定理。  相似文献   

3.
本文利用广义常微分方程的平均化定理,建立脉冲滞后泛函微分方程周期及非周期的平均化定理。  相似文献   

4.
李宝麟  田瑞 《数学学报》2023,(4):707-716
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.  相似文献   

5.
泛函微分方程的全局稳定周期解   总被引:2,自引:0,他引:2  
王克 《数学学报》1994,37(4):570-573
本文综合运用相空间理论,泛函分析方法和李雅普诺夫第二方法,研究具无限时滞的泛函微分方程周期解的存在性,唯一性和稳定性问题,得到了新的结果.  相似文献   

6.
具有超前和滞后的泛函微分方程的周期解   总被引:1,自引:0,他引:1  
李勇 《应用数学学报》1992,15(3):297-305
考虑具有超前和滞后的泛函微分方程的ω-周期解的存在性问题,其中L_i,R_j,φ_k,ψ_k:R→R(i=1,…,m_1,j=1,…1,…,m_2,k=1,…,m_3)是连续的ω周期函数,D_i:R~2→R~(n×n)连续,关于t以ω为周期;f:R×R~n×…×R~n→R~n连续,关于t以ω为周期;m_1,m_2,m_3为正整数,ω为正常数。 近些年来,人们利用Liapunov第二方法研究常微分方程和具有有限滞后或无限滞  相似文献   

7.
在一定的条件下, 测度微分方程与广义常微分方程等价, 因此广义常微分方程的一些理论可应用于测度微分方程. 很多材料已经描述了广义常微分方程的解相对于初始条件的可微性, 并且也广泛的应用于不同类型的方程. 为此, 本文利用广义常微分方程的解相对于初始条件的可微性建立了测度微分方程的解相对于初始条件的可微性.  相似文献   

8.
中立型泛函微分方程的周期解   总被引:1,自引:1,他引:0  
对于中立型泛函微分方程,证明了解的毕竟有界性蕴含周期解的存在性,把常微分方程中著名的Yoshizawa周期解存在定理推广到中立型泛函微分方程,然后利用所得结果给出一类产生于电力系统的中立型时滞泛函微分方程周期解存在惟一与吸引的条件。  相似文献   

9.
马学敏  李宝麟 《应用数学》2017,30(3):684-692
本文中, 我们通过利用平均化方法,将非自治常微分方程转化成自治方程, 刻画了其平均化过程, 得到非自治方程的平均化方程, 而且利用Henstock-Kurzweil积分, 建立了Carathéodory方程的周期和非周期的平均化定理.  相似文献   

10.
一定条件下,测度微分方程与广义常微分方程等价,从而,广义常微分方程的一些理论可应用于测度微分方程,相关文献已讨论了广义常微分方程的解相对于初始条件的可微性,而且这一理论可应用于其他类型的方程.为此本文中,利用广义常微分方程的解相对于初始条件的可微性得到测度微分方程的解相对于初始条件的可微性定理.  相似文献   

11.
We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.  相似文献   

12.
The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations without the linear growth condition by the use of the Lyapunov functions. However, there is no such result for stochastic functional equations with infinite delay. The main aim of this paper is to establish the existence-and-uniqueness theorems of global solutions for stochastic functional differential equations with infinite delay.  相似文献   

13.
In this paper, by measure theory, we introduce and investigate the concepts of (Stepanov-like) $(\mu,\nu)$-pseudo almost automorphic of class $r$ and class infinity, respectively. As applications, we establish some sufficient criteria for the existence, uniqueness of pseudo almost automorphic mild solutions to two-term fractional functional differential equations with finite or infinite delay. The working tools are based on the generalization of semigroup theory, Banach contraction mapping principle and Leray-Schauder alternative theorem. Finally, we explore the same topic for a fractional partial functional differential equation with delay.  相似文献   

14.
For linear functional difference equations, we obtain some results on the asymptotic behavior of solutions, which correspond to a Perron-type theorem for linear ordinary difference equations. We also apply our results to Volterra difference equations with infinite delay.  相似文献   

15.
We introduce measure functional differential equations with infinite delay and an axiomatically described phase space. We show how to transform these equations into generalized ordinary differential equations whose solutions take values in a suitable infinite-dimensional Banach space. Even in the special case of functional equations with finite delay, our result improves the existing one by imposing weaker conditions on the right-hand side.  相似文献   

16.
无限时滞中立型随机泛函微分方程解的存在唯一性   总被引:1,自引:1,他引:0  
有限时滞随机泛函微分方程的存在唯一性已经得到较多的研究,但对于无限时滞随机泛函微分方程的性质极少.本文在不需要线性增长条件,在一致Lipschitz条件下证明了无限时滞中立型随机泛函微分方程的存在唯一性,给出了精确解和近似解的误差估计,最后给出了解的矩估计.  相似文献   

17.
In the main result of this paper, some sharp conditions are obtained for global attractivity in a scalar perturbed linear delay differential equation. The proof of the main theorem is based on a new estimate for the infinite integral of the absolute value of the fundamental solution of a linear delay differential equation. We also derive sufficient conditions for asymptotic stability of a system of linear delay differential equations.  相似文献   

18.
Oscillation of first order delay differential equations   总被引:7,自引:0,他引:7  
We introduce a new technique to analyze the generalized characteristic equations to obtain some infinite integral conditions for oscillation of the nonautonomous delay differential equations.

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19.
The Banach fixed point theorem and the nonlinear alternative of Leray-Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay.  相似文献   

20.
The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs). Firstly, we establish stochastic versions of the well-known Picard local existence-uniqueness theorem given by Driver and continuation theorems given by Hale and Driver for functional differential equations (FDEs). Then, we extend the global existence-uniqueness theorems of Wintner for ordinary differential equations (ODEs), Driver for FDEs and Taniguchi for stochastic ordinary differential equations (SODEs) to SFDEs. These show clearly the power of our new results.  相似文献   

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