OSCILLATION CRITERIA FOR STRONGLY SUPERLINEAR AND STRONGLY SUBLINEAR HIGHER ORDER DYNAMIC EQUATIONS ON TIME SCALES

We establish some new criteria for the oscillation of even order nonlinear dynamic equation. We study the case of strongly super-linear and the case of strongly sub-linear subject to various conditions.     

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH p-LAPLACIAN AND DAMPING

This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping（r（t）φ（x^△（t））^△＋p（t）φα（x^△α（t）＋q（t）f（xδ（t））=0on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results.     

OSCILLATION CRITERIA FOR SECOND ORDER QUASILINEAR NEUTRAL EQUATION

We present some new oscillation criteria for second order neutral delay differential equations with distributed deviating argument using the Riccati technique and some inequalities. The results obtained improve and extend some known results.     

OSCILLATION FOR NONLINEAR SECOND-ORDER DYNAMIC EQUATIONS ON TIME SCALES

Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.     

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR NEUTRAL PERTURBED DYNAMIC EQUATIONS ON TIME SCALES

In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example that dwells upon the sharp conditions of our result is also included.     

OSCILLATION CRITERIA FOR SECOND ORDER NEUTRAL DIFFERENCE EQUATION WITH CONTINUOUS VARIABLE

In this paper, we are concerned with the second order neutral difference equation with continuous variable. Using the integral transformation and generalized Riccati transformation, we obtain some oscillation criteria.     

OSCILLATION CRITERIA FOR A CLASS OF HIGHER ORDER NEUTRAL DIFFERENTIAL EQUATIONS

We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and     

AN OSCILLATION CRITERION FOR SECOND ORDER SUBLINEAR DIFFERENTIAL EQUATIONS

ＡＮＯＳＣＩＬＬＡＴＩＯＮＣＲＩＴＥＲＩＯＮＦＯＲＳＥＣＯＮＤＯＲＤＥＲＳＵＢＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＬｉＷａｎｔｏｎｇ（ＺｈａｎｇｙｅＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，７３４０００）ＱｕａｎＨｏｎｇｓｈｕｎ（Ｌａｎｚ...     

JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS

In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.     

一类四阶差分方程振动性的充分必要条件

本文给出了四阶差分方程△＾２（ｒｎ△＾２ｙｎ）＋ｆ（ｎ,ｙｎ）＝０,ｎ＝０,１,２,…的所有解（有界解）振动的一些充分条件和必要条件。     

OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

OSCILLATIONS OF FOURTH ORDER ODE WITH IMPULSES

Sufficient conditions to guarantee the oscillations of fourth order ODE with impulses are obtained. The importance of the impulsive effect on the oscillations of higher order differential equations is stressed.     

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.     

测度链上一类三阶半线性中立型时滞动力方程的振动准则

利用广义Riccati代换及时标上一些分析技巧给出时标上一类三阶半线性动力方程的振动准则,并利用例子说明其结果的可用性,推广了一些已知的二阶或三阶动力方程振动性的结果.     

NEW OSCILLATION CRITERIA RELATED TO EULER'S INTEGRAL FOR CERTAIN NONLINEAR DIFFERENTIAL EQUATION

Using the integral average technique and a new function,some new oscillation criteria related to Euler integral are obtained for second order nonlinear differential equations with damping and forcing. Our results are of a higher degree of generality than some previous results. Information about the distribution of the zeros of solutions to the system is also obtained.     

一类二阶时滞微分方程的振动性判据

本文从不同的角度研究一类二阶时滞微分方程的振动性，得到了一切解振动性的充分条件。改善了文［１］、［２］的工作．     

二阶非线性阻尼微分方程解的振动性质

本文研究了一类二阶非线性阻尼微分方程解的振动性,利用分类讨论和分析的方法,建立了两个新的振动性定理,推广和改进了已有的结果.     

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 →∞.     

OSCILLATION CRITERIA FOR EVEN ORDER DELAY DIFFERENTIAL EQUATIONS WITH NONLINEAR TERM

By Riccati transformation, we establish some new oscillation criteria for a class of even order delay differential equations with nonlinear term. In some sense, the results obtained extend some known results in the literature.