共查询到20条相似文献,搜索用时 31 毫秒
1.
利用广义Riccati代换给出了时标上一类三阶中立型动力方程的振动准则,其结果不仅得到了几个振动解存在的条件,也拓展了一些已有的结论,在最后还给出了几个例子来验证结论. 相似文献
2.
杨甲山 《数学物理学报(A辑)》2014,34(2):393-408
研究了时间测度链上一类具正负系数和阻尼项及非线性中立项的二阶变时滞非线性动力方程的振荡性.利用时间测度链上的有关理论及广义Riccati变换,结合大量不等式技巧,建立了该方程若干新的振动准则,这些准则不仅推广和改进了一些已知的结果,而且在时间测度链上统一了二阶非线性时滞阻尼微分方程和二阶非线性时滞阻尼差分方程的振动性质. 相似文献
3.
YANG Jia-shan 《数学季刊》2014,(3):447-456
This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results. 相似文献
4.
Here we solve two problems presented in paper [9] (C C Tisdell and A Zaidi, Basic qualitative and quantitative results for
solutions to nonlinear, dynamic equations on time scales with an application to economic modelling, Nonlinear Anal.
68 (2008) 3504–3524). We study existence and uniqueness of solutions for delay systems and first-order dynamic equations of
the form x
Δ = f (t,x,x
σ
) on time scales by using the Banach’s fixed-point theorem. Some examples are presented to illustrate the efficiency of the
proposed results. 相似文献
5.
Jiashan Yang 《Journal of Applied Mathematics and Computing》2013,43(1-2):445-466
The oscillation of certain third-order nonlinear variable delay functional dynamic equations with nonlinear neutral on time scales is discussed in this article. By using the generalized Riccati transformation and a lot of inequality techniques, some new oscillation criteria for the equations are established. Many of the results are new for the corresponding third-order difference equations and differential equations are as special cases. Some examples are given to illustrate the importance of our results. 相似文献
6.
Shoufu Li 《中国科学A辑(英文版)》2003,46(5):662-674
B-stability andB-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra functional differential equations (VFDEs) are established
which provide unified theoretical foundation for the study of Runge-Kutta methods when applied to nonlinear stiff initial
value problems (IVPs) in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential
equations (IDEs) and VFDEs of other type which appear in practice. 相似文献
7.
Gleiciane da Silva Aragão Sergio Muniz Oliva 《Journal of Differential Equations》2012,253(9):2573-2592
In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction–diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter ? goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. 相似文献
8.
研究时标T上的一类具非正中立项的非线性非自治二阶动力方程的动力学性质.利用时标上的有关理论,并结合一些经典不等式,得到了该方程的一些新的动力学性质,进一步推广和完善了动力方程的动力学性质. 相似文献
9.
By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations with damping on a time scale. Our results extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. 相似文献
10.
11.
利用广义Riccati变换及完全平方技巧,讨论了一类时标上的二阶非线性变时滞动力系统的振动性,获得了新的振动准则. 相似文献
12.
13.
For the past few decades, the stability criteria for the stochastic differential delay equations (SDDEs) have been studied intensively. Most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability criterion for highly nonlinear hybrid stochastic differential equations is investigated in Fei et al. (2017). In this paper, we investigate a class of highly nonlinear hybrid stochastic integro-differential delay equations (SIDDEs). First, we establish the stability and boundedness of hybrid stochastic integro-differential delay equations. Then the delay-dependent criteria of the stability and boundedness of solutions to SIDDEs are studied. Finally, an illustrative example is provided. 相似文献
14.
Hamid Reza Marzban Hamid Reza Tabrizidooz 《Communications in Nonlinear Science & Numerical Simulation》2012,17(1):100-109
The hybrid function approximation method for solving Hutchinson’s equation which is a nonlinear delay partial differential equation, is investigated. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials based on Legendre-Gauss-type points are presented and are utilized to replace the system of nonlinear delay differential equations resulting from the application of Legendre pseudospectral method, by a system of nonlinear algebraic equations. The validity and applicability of the proposed method are demonstrated through two illustrative examples on Hutchinson’s equation. 相似文献
15.
Comparison theorem and explicit sufficient conditions are obtained for oscillation and nonoscillation of solutions of nonlinear impulsive delay differential equations which can be utilized to population dynamic models. Our results in this paper generalize and improve several known results. 相似文献
16.
《中国科学 数学(英文版)》2015,(7)
We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves related contributions to the subject. An example is provided to illustrate assumptions in our theorem are less restrictive. 相似文献
17.
We propose a new approach for deriving nonlinear evolution equations solvable by the inverse scattering transform. The starting point of this approach is consideration of the evolution equations for the scattering data generated by solutions of an arbitrary nonlinear evolution equation that rapidly decrease as x±. Using this approach, we find all nonlinear evolution equations whose integration reduces to investigation of the scattering-data evolution equations that are differential equations (in either ordinary or partial derivatives). In this case, the evolution equations for the scattering data themselves are linear and moreover solvable in the finite form. 相似文献
18.
This paper addresses the design of H
∞ state feedback controllers for a class of nonlinear time-varying delay systems. The interesting features here are that the
system in consideration is nonautonomous with fast-varying delays, the delay is also involved in the observation output, and
the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using the proposed
Lyapunov functional approach, neither a controllability assumption nor a bound restriction on nonlinear perturbations is required
to obtain new sufficient conditions for the H
∞ control. The conditions are derived in terms of a solution to the standard Riccati differential equations, which allows for
simultaneous computation of the two bounds that characterize the stability rate of the solution.
This work was supported by the National Foundation for Science and Technology Development, Vietnam and the Center of Excellence
for Autonnomous Systems funded by the Australian Research Council, Australia. 相似文献
19.
This paper is concerned with the analytic and numerical stability of a class of nonlinear neutral delay differential equations.
A sufficient condition for the stability of the problems itself is given. The numerical stability results are obtained for
A-stable one-leg methods when they are applied to above mentioned problems. Numerical examples are given to confirm our theoretical
results. 相似文献
20.
Murat Ad?var Elvan Ak?n Bohner 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7519-7531
This paper aims to introduce Halanay type inequalities on time scales. By means of these inequalities we derive new global stability conditions for nonlinear dynamic equations on time scales. Giving several examples we show that besides generalization and extension to q-difference case, our results also provide improvements for the existing theory regarding differential and difference inequalities, which are the most important particular cases of dynamic inequalities on time scales. 相似文献