Lyapunov-type inequalities for a class of higher-order linear differential equations

In this paper, we obtain some Lyapunov-type inequalities for a class of higher-order linear differential equations. The results of this paper generalize and improve some earlier results on this topic.     

一阶中立型线性微分系统解的振动性

本文给出一类一阶中立型线性微分系统解振动的充分条件 ,改进和推广了文 [1 ]的工作 .     

脉冲强迫非线性时滞微分方程的渐近性

本文研究一类脉冲强迫非线性时滞微分方程的渐近性,所得结果不仅适用于线性方程和非线性方程,强迫方程和非强迫方程,脉冲方程和非脉冲方程,而且改进了最近文献［８］的主要结果．     

Lyapunov-type inequalities for a class of higher-order linear differential equations with anti-periodic boundary conditions

In this paper, we obtain some new Lyapunov-type inequalities for a class of higher-order linear differential equations with anti-periodic boundary value condition, the results of this paper are new and generalize and improve some early results in the literature.     

Local first integrals of differential systems and diffeomorphisms

In this paper using theory of linear operators and normal forms we generalize a result of Poincaré [11] about the non-existence of local first integrals for systems of differential equations in a neighbourhood of a singular point. As an application of the generalized result, and under more weak conditions we obtain a result of Furta [8] about local first integrals of semi-quasi-homogeneous systems. Moreover, for diffeomorphisms and periodic differential systems we give definitions of their first integrals, and generalize the previous results about systems of differential equations to diffeomorphisms in a neighbourhood of a fixed point and to periodic differential systems in a neighbourhood of a constant solution.     

New Lyapunov‐type inequalities for a class of even‐order linear differential equations

In this paper, we obtain some new Lyapunov‐type inequalities for a class of even‐order linear differential equations, the results are new and generalize and improve some early results in this field.     

On Lyapunov-type inequality for quasilinear systems

In this paper, we sketch some recent developments in the theory of Lyapunov-type inequalities and present some new results relating to a quasilinear system, special cases of which contain some well-known differential equations such as half-linear and linear equations. Our result generalize the Lyapunov-type inequality given in [18].     

$[p, q]$级整函数系数的二阶线性微分方程的复振荡

In this paper, the authors investigate the zeros and growth of solutions of second order linear differential equations with entire coefficients of [p, q]-order and obtain some results which improve and generalize some previous results.     

Asymptotic Behavior of Forced Nonlinear Delay Differential Equations with Impulses

The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses Our results, which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations, improve and generalize the known results recently obtained in [8]. Received September 7, 1997, Revised May 26, 1998, Accepted July 15, 1998     

Tightened reachability constraints for the verification of linear hybrid systems

In this paper, we first generalize reachability constraints for linear differential equations, then tighten them by using the information of multiplicity of the eigenvalues and eigenvectors of such equations and put them into our constraint based approach for safety verification of hybrid systems that employs recursive reasoning to improve the method of constraint propagation based abstraction refinement.     

Consistent solutions of linear equations in variational derivatives

In this paper, we consider the classical existence problem for consistent and uniformly consistent solutions of linear equations in variational derivatives. In particular, we generalize several results obtained by V. V. Zhikov and B. A. Shcherbakov concerning the existence of almost-periodic, consistent, and uniformly consistent solutions of ordinary differential equations.     

GENERALIZED RICCATI TRANSFORMATION AND OSCILLATION FOR LINEAR DIFFERENTIAL EQUATIONS WITH DAMPING

Using generalized Riccati transformation, some new oscillation criteria for damped linear differential equations are established. These results improve and generalize some known oscillation criteria due to A.Wintner, I.V.Kamenev for the undamped linear differential equations, and Sobol, J.S.W.Wong for the damped linear differential equations.     

Asymptotic behaviour and zeros of solutions of linear differential equations

Summary. Certain classes of linear differential equations are investigated for which the distribution of zeros of their solutions determines their asymptotic behaviour. These results generalize those already obtained for the second order linear differential equations to equations of arbitrary order.     

时不变和时变的Caputo分数阶时滞微分系统的常数变易公式

This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall＇s integral inequality. The variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform method. In terms of the superposition principle of linear systems and fundamental solution matrix, we also establish the variation of constant formula for linear time varying fractional delay differential systems. The obtained results generalize the corresponding ones of integer-order delayed differential equations.     

Oscillation Result for Some Non-homogeneous Linear Differential Equations and Its Application

This paper investigates solutions of some non-homogeneous linear differential equations, which have non-homogeneous term as the small function of solution. Using the similar method, we can generalize the result of G.Gundersen and L.Z.Yang.     

On the reducibility of linear differential equations with quasiperiodic coefficients which are degenerate

This paper proves the reducibility of a class of linear differential equations with quasiperiodic coefficients which are degenerate with respect to a small perturbation parameter. Our results generalize some that were obtained by Jorba and Simó.

     

Existence results of second order impulsive functional differential equations with infinite delay and fractional damping

In this paper we prove the existence, uniqueness, regularity and continuous dependence of mild solutions for second order impulsive functional differential equations with infinite delay and fractional damping in Banach spaces. We generalize the existence theorem of integer order differential equations to the fractional order case. The results obtained here improve and generalize some known results.     

Initial value methods in the theory of Fredholm integral equations III. The nonlinear eigenvalue problem

In this paper, it is shown that the method introduced recently by Kalaba and Scott for solving nonlinear characteristic value problems for integral operators is equivalent to a nonlinear characteristic value problem for a matrix. This is demonstrated by finding the explicit solution to the set of differential equations used by them. The results generalize those proved recently by the author for the linear problem.     

On Liapunov-type inequality for certain higher-order differential equations

In this paper, we generalize the well-known Liapunov-type inequality for a class of third-order differential equations without damping force to 2n+1 order differential equations.     

Existence of dichotomies and invariant splittings for linear differential systems I

This paper is concerned with linear time-varying ordinary differential equations. Sufficient conditions are given for the existence of an exponential dichotomy for a class of equations which includes those with Bohr almost-periodic coefficients. The problem is treated in the context of linear skew-product flows, where it becomes clear how to generalize to the case of fiber-preserving flows on vector bundles. Both continuous and discrete flows are treated and the results apply to the linearized variational equation for a time-varying vector field on a manifold as well as the linearization of a diffeomorphism acting on a manifold. Sufficient conditions are given for a diffeomorphism on a manifold to be an Anosov diffeomorphism. For linear skew-product flows arising from ordinary differential equations our theory is a partial generalization of Floquet theory to the almost-periodic case.