ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.     

AN INSTABILITY THEOREM FOR A CERTAIN SEVENTH-ORDER DIFFERENTIAL EQUATION

The object of the paper is to establish an instability theorem for seventh-order differential equations of the form (1.10). The proof is based on the use of Krasovskii criteria.     

ON THE STABILITY OF SOLUTIONS TO A CERTAIN FOURTH-ORDER VECTOR DELAY DIFFERENTIAL EQUATION

In this paper, by constructing a Lyapunov functional, sufficient conditions for the uniform stability of the zero solution to a fourth-order vector delay differential equation are given.     

ON THE EXISTENCE OF PERIODIC SOLUTIONS TO A CERTAIN FOURTH-ORDER NONLINEAR DIFFERENTIAL EQUATION

In this paper, we consider a certain fourth-order nonlinear ordinary differential equation. Some sufficient conditions which guarantee the existence of at least one ω-periodic solution to the system are obtain.     

ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF A CERTAIN FOURTH-ORDER DIFFERENTIAL EQUATION

The present paper establishes sufficient conditions for the uniformly bounded of any solution of (1.1) and which tend to zero as t → ∞.     

THE INSTABILITY OF A DIFFERENTIAL EQUATION WITH ODD ORDER

Our work pays much attention to the instability of an nth-order differential equation whose coefficients are not all constants, where n is an odd integer and n ≥ 3. Finally, we obtained a sufficient condition of the instability.     

ON STABILITY OF SOLUTION OF A CERTAIN FOURTH ORDER VECTOR DIFFERENTIAL EQUATIONS

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A STABILITY THEOREM FOR A CERTAIN FOURH-ORDER VECTOR DIFFERENTIAL FQUATION

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ON THE BOUNDEDNESS OF A CERTAIN SYSTEM OF FIFTH-ORDER DIFFERENTIAL EQUATION

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A STABILITY RESULT ON SOLUTIONS TO CERTAIN FOURTH ORDER NON-HOMOGENEOUS DIFFERENTIAL EQUATIONS

In this paper,we study the fourth order non-homogeneous differential equations x(4) + f1()+ f2() + f3(■) + f4(x) = p(t,x,■,,x),and obtain suffcient conditions,under which the solutions to the system tend to zero as t →∞.     

一类高阶齐次线性微分方程解的零点

本文研究一类整函数系数高阶齐次线性微分方程解的零点分布.利用Nevanlinna值分布理论,得到当系数A_(k-1)的增长性起主要支配作用时,方程f~((k))+A_(k-1)f~((k-1))+···+A_0f=0任意超越解的零点收敛指数为无穷,推广了Langley和Bank等人的结果.     

UNSTABLE SOLUTIONS TO A CLASS OF VECTOR DIFFERENTIAL EQUATIONS OF SIXTH ORDER

In this paper, we consider a class of nonlinear vector differential equations of sixth order. By constructing appropriate Lyapunov functions, the non-existence of periodic solutions is established. Moreover, we provide an example to show the feasibility of our results. Our results extend and improve two related results in the previous literature from scalar cases to vectorial cases.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, a class of higher order linear differential equation is investigated. The order and the hyper-order of the solutions of the equation are exactly estimated under some certain conditions.     

ON THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, we consider a higher order differential equation and obtain a precise estimate of the order of growth and the hyper-order of solutions to the equation.     

REGULARITY OF SOLUTIONS TO NONLINEAR TIME FRACTIONAL DIFFERENTIAL EQUATION

We find an upper viscosity solution and give a proof of the existence-uniqueness in the space C^∞（t∈（0,∞）;H2^s＋2（R^n））∩C^0（t∈[0,∞）;H^s（R^n））,s∈R,to the nonlinear time fractional equation of distributed order with spatial Laplace operator subject to the Cauchy conditions ∫0^2p（β）D＊^βu（x,t）dβ=△xu（x,t）＋f（t,u（t,x））,t≥0,x∈R^n,u（0,x）=φ（x）,ut（0,x）=ψ（x）,（0.1） where △xis the spatial Laplace operator,D＊^β is the operator of fractional differentiation in the Caputo sense and the force term F satisfies the Assumption 1 on the regularity and growth. For the weight function we take a positive-linear combination of delta distributions concentrated at points of interval （0, 2）, i.e., p（β） =m∑k=1bkδ（β-βk）,0〈βk〈2,bk〉0,k=1,2,…,m.The regularity of the solution is established in the framework of the space C^∞（t∈（0,∞）;C^∞（R^n））∩C^0（t∈[0,∞）;C^∞（R^n））when the initial data belong to the Sobolev space H2^8（R^n）,s∈R.     

复非线性代数微分方程解的增长级(英文)

本文研究了一类非线性微分方程的解的增长级的问题.利用亚纯函数的Nevanlinna值分布理论和Wiman-Valiron整函数理论的方法,获得了比以往文献更为精确,更为一般的结论,推广了Gol’dberg,Barsegian,Hayman以及Korhonen等作者的一些结果.     

AN INSTABILITY THEOREM FOR A KIND OF SEVENTH ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

This paper considers a kind of seventh order nonlinear differential equations with a deviating argument.By means of the Lyapunov direct method,some sufficient conditions are established to show the instability of the zero solution to the equation.Our result is new and complements the corresponding result of [5].     

一类三阶时滞微分方程解的渐进稳定性

本文研究了三阶非线性时滞微分方程解的渐近稳定性.利用Lyapunov泛函,得到了微分方程的零解是渐进稳定的,这一结果推广了文献[2]的结果.     

一类三阶时滞微分方程解的渐进稳定性

本文研究了三阶非线性时滞微分方程解的渐近稳定性. 利用Lyapunov 泛函, 得到了微分方程的零解是渐进稳定的, 这一结果推广了文献[2] 的结果.