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Oscillation Theorems of the second order Linear Matrix Differential System with Damping

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Acta Mathematica Sinica,English Series 2005年第1期21卷 17-30页

作者： QiGuiYANG DepartmentofAppliedMathematics SouthChinaUniversityofTechnologyGuangzhou510640P.R.China

By using the Riccati technique and the technique, new oscillation criteriaare obtained for the second order matrix differential system (P(t)Y'(t))' + r(t)P(t)Y(t) + Q(t)Y (t)= 0, t ≥ t_0. These results in the present paper generalize and improve many known ***, some results are different from the most known ones in the sense that they are based onthe information only on a sequence of subintervals of [t 0,), rather than on the whole half–*** particular, our results complement a number of existing results and handle the case that is notcovered by the known criteria.

关键词： Oscillation Matrix differential system second order

Boundedness of Solutions of second order Nonlinear Dynamic Equations

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 505-520页

作者： Ye-hui HUANG Zhi-ting XU School of Mathematical Sciences South China Normal University

This paper deals with the boundedness of the solutions of the following dynamic equations andon a time scale T. By using the Bellman integral inequality, we establish some sufficient conditions for bound- edness of solutions of the above equations. Our results not only unify the boundedness results for differential and difference equations but are also new for the q-difference equations.

关键词： boundedness nonlinear dynamic equations time scale solution second order

FORCED OSCILLATION OF second order DIFFERENTIAL EQUATIONS WITH MIXED NONLINEARITIES

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Acta Mathematica Scientia 2011年第2期31卷 613-626页

作者： Taher S. Hassan Lynn Erbe Allan Peterson Department of Mathematics Faculty of Science Mansoura University Department of Mathematics University of Nebraska-Lincoln

This article is concerned with the oscillation of the forced second order differ- ential equation with mixed nonlinearities（a（t）（x＇（t））γ）＇＋po（t）xγ（go（t））＋n∑t=1pi（t）｜x（gi（t））｜αi sgn x（gi（t））=e（t）,where γ is a quotient of odd positive integers αi〉0,i=1,2 ……n,a,e,and pi ∈ C（[0,∞）R）,a（t）〉0,gi：R→R are positive continuous functions on R with lim gi （t）=∞,i=0,1,……,n. Our results generalize and improve the results in a recent article by Sun and Wong[29].

关键词： Oscillation functional differentail equations second order

Averaging Technique for the Oscillation of second order Damped Elliptic Equations

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Acta Mathematica Sinica,English Series 2008年第5期24卷 829-842页

作者： Zhi Ting XU School of Mathematical Sciences South China Normal University Guangzhou 510631 P. R. China

By using the averaging technique, we establish some oscillation theorems for the second order damped elliptic differential equation N↑∑↓i,j=1 Di[AIY（x）Djy]＋N↑∑↓i=1 bi（x）Diy＋c（x）f（y）=0 which extend and... 详细信息

关键词： oscillation averaging technique second order elliptic differential equation damped

Philos-type Oscillation Theorems for second order Damped Elliptic Equations

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Acta Mathematicae Applicatae Sinica 2009年第2期25卷 291-304页

作者： Zhi-ting Xu School of Mathematical Sciences South China Normal University Guangzhou 510631 China

Using general means, we establish several new Philos-type oscillation theorems for the second order damped elliptic differential equationΣi,j=1 N Di[aij（x）Djy]＋Σi=1 N bi（x）Diy＋c（x）f（y）=0under quite general assumptions. The obtained results are extensions of the well-known oscillation results due to Kamenev, Philos, Yan for second order linear ordinary differential equations and improve recent results of Xu, Jia and Ma.

关键词： Oscillation elliptic differential equations second order damped

Oscillation of second order Delay Differential Equations with Nonlinear Neutral Term

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Chinese Quarterly Journal of Mathematics 2006年第2期21卷 271-277页

作者： XU Zhi-ting JIN Chu-hua School of Mathematical Sciences South China Normal University Guangzhou 510631 China Department of Applied Mathematics Guangdong University of Technology Guangzhou 510090 China

By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral dela... 详细信息

关键词： oscillation delay differential equation nonlinear neutral term second order

Existence and Uniqueness of Periodic Solutions for a Kind of second order Neutral Functional Differential Equations with Constant Delays

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Acta Mathematicae Applicatae Sinica 2006年第2期22卷 287-296页

作者： Bing-wen Liu Li-hong Huang Department of Mathematics Hunan University of Arts and Science Changde 415000 China College of Mathematics and Econometrics Hunan University Changsha 410082 China

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays o... 详细信息

关键词： second order neutral functional differential equations constant delay Periodic solutions coincidence degree,

A second order DIFFERENCE SCHEME WITH NONUNIFORM MESHES FOR NONLINEAR PARABOLIC SYSTEM

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Journal of Systems Science & Complexity 2003年第2期16卷 199-208页

作者： WANZhengsu CHENGuangnan DepartmentofMathematics ShanghaiUniversityShanghai200436China LaboratoryofComputationalPhysics InstituteofAppliedPhysicsandComputationalMathematicsP.O.Box8009Beijing100088China

In this paper, a difference scheme with nonuniform meshes is established for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in spaces... 详细信息

关键词： second order difference nonuniform meshes

OSCILLATION THEOREMS FOR A CLASS OF second order NEUTRAL DIFFERENTIAL EQUATIONS OF EMDEN-FOWLER TYPE

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Annals of Differential Equations 2009年第3期25卷 371-378页

作者： Jinchang Yu (Software College,Dongguan University of Technology,Dongguan 523808,Guangdong) Software College Dongguan University of TechnologyDongguan 523808Guangdong

Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous ... 详细信息

关键词： oscillation neutral differential equation Emden-Fowler type averaging technique second order