BASIC THEORY OF IMPULSIVE DIFFERENTIAL EQUATION WITH DELAY

ＢＡＳＩＣＴＨＥＯＲＹＯＦＩＭＰＵＬＳＩＶＥＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＤＥＬＡＹＸｉｅＹａｎｌｉｎ（谢彦麟）（ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，华南师范大学，邮编：５１０６３１）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓ...     

OSCILLATION OF NONLINEAR HYPERBOLIC DIFFERENTIAL EQUATION WITH IMPULSES

In this paper, oscillatory properties of solutions for nonlinear impulsive hyperbolic differential equation are investigated and some new sufficient conditions are established.     

PERIODIC CHARACTER OF A DIFFERENCE EQUATION WITH MAXIMUM

We study the periodicity of the positive solutions of a class of difference equations with maximum. We prove that every positive solutions of these equations are eventually periodic.     

OSCILLATIONS OF NTH-ORDER NEUTRAL EQUATION WITH CONTINUOUSDISTRIBUTED DEVIATING ARGUMENTS

AMSSubjectClassification34C10,34K401IntroductionInthispaper,wediscussoscillatorybehaviorofthefollowingnibordernonlinearequationwherenisevenandTisapositiveconstant.'TheProjectsupportedbyNaturalScienceFOundationofHebeiProvince(197091).ForEq.(l),thecasen=2an…     

OSCILLATIONS OF HIGHER ORDER ORDINARY DIFFERENTIAL EQUATION WITH IMPULSES

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

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.     

OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY

In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.     

EXPONENTIAL STABILITY OF A PARTIAL DIFFERENCE EQUATION WITH NONLINEAR PERTURBATION

1.IntroductionPartialdifferenceequationshaveappearedinmanybranchesofmathematics.Indeed,LagrangeandLaplacehavediscussedsuchequationsinrelationtoprobability[1],Couralltetal.[z]haveconsideredtheminrelationtodifferentialequationsofmathematicalphysics.Inrecenty6ars,signalandimageprocessingtheory(seee.g.[3])alsomakesuseofthetheoryofpartialdchrenceequations.OscillationtheoryfortheseeqllationshasbeeninvestigatedbyanUmberofauthorsrecelltly[4].However,asystematicinvestigationofthestabilitytheoryofpart…     

ANALYTIC SOLUTIONS OF AN ITERATIVE EQUATION WITH FIRST ORDER DERIVATIVE

This paper is concerned with a nonlinear iterative equation with first order derivative. By construction a convergent power series solution, analytic solutions for the original equation are obtained.     

OSCILLATION OF NONLINEAR IMPULSIVE PARABOLIC DIFFERENTIAL EQUATION WITH SEVERAL DELAYS

In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equation are investigated and a series of new sufficient conditions is established.     

BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

ＢＯＵＮＤＡＲＹＬＡＹＥＲＥＳＴＩＭＡＴＩＯＮＯＦＡＳＩＮＧＵＬＡＲＰＲＯＢＬＥＭＷＩＴＨＬＩＭＩＴＥＱＵＡＴＩＯＮＯＦＯＲＤＥＲ２ＨＥＣＨＥＮＧ（何成）ＺＨＡＮＧＷＥＩＴＡＯ（张维弢）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ｃｈｉｎｅ...     

GLOBAL EXISTENCE AND STABILITY OF FUNCTIONAL DIFFERENTIAL EQUATION WITH IMPULSES

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐｒｅｓｅｎｔｐａｐｅｒ，ｗｅｄｅａｌｗｉｔｈａｎｉｍｐｕｌｓｉｖｅｆｕｎｃｔｉｏｎａｌｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ（ＩＦＤＥ）ｉｎｔｈｅａｆｏｒｍ：ｄｘｄｔ＝ｆ（ｔ，ｘｔ），ｔ≥ｔ０，ｘ（ｔｋ）－ｘ（ｔ...     

HORSESHOE MOTIONS AND SUBHARMONICS OF THE EQUATION OF J-J TYPE WITH SMALL PARAMETERS

In this paper,we have proved the existence of horseshoe motions and subharmonic motions of the equation of a Josephson junction with small parameters by using Melnikov's method.     

SOLITON SOLUTION OF NONLINEAR SCHRODINGER EQUATION WITH HIGHER ORDER DISPERSION TERMS

It is shown in this paper that if parameters β1,β2 and β3 of a nonlinear Schrodinger equation with higher order dispersion terms (HNLS) satisfy the condition: 6β1-β2-2β3(1- 6β1k)= 0, k a real constant, then the fundamental soliton solutions of the HNLS equation exist. The exact soliton solutions are given and the relation between this condition and the known results inthe literature is also discussed.     

THE BOUNDARY VALUE PROBLEMS OF A CLASS OF ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT

The boundary value problems of a class of elliptic equation with a curveof turning point are considered. Using the method of multiple scales and thecomparison theorem, the asymptotic behavior of solution for the boundary valueproblem is studied.     

CONDITIONS OF ORTHOGONALITY AND STABILITY ASSOCIATED WITH THE GENERAL REFINEMENT EQUATION

ＣＯＮＤＩＴＩＯＮＳＯＦＯＲＴＨＯＧＯＮＡＬＩＴＹＡＮＤＳＴＡＢＩＬＩＴＹＡＳＳＯＣＩＡＴＥＤＷＩＴＨＴＨＥＧＥＮＥＲＡＬＲＥＦＩＮＥＭＥＮＴＥＱＵＡＴＩＯＮＺｈａｎｇＱｉｎｇ（张青）（ＨｕｂｅｉＣｏｌｌｅｇｅｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃ...     

LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF THREE-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

The three-dimensional nonlinear SchrSdinger equation with weakly damped that possesses a global attractor are considered. The dynamical properties of the discrete dynamical system which generate by a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete dynamical system.     

DYNAMICAL BEHAVIOR IN THE EQUATION OF J-J TYPE WITH LARGE DC-CURRENT

This paper studies the dynamical behavior in the equation of J-J type with largedc-current by using rigorous mathematical analysis.The problem is completly solved.The conclusion is no chaotic motion takes place,every trajectory is asymptotically periodicor quasi-periodic.