ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved.     

OSCILLATION OF A NONLINEAR DELAY DIFFERENTIAL EQUATION WITH NONLINEAR NEUTRAL TERM

This paper is concerned with the following nonlinear delay differential equation with nonlinear neutral term[h(t)(y(t) +φ(t,y(τ(t)))']' + q(t)f(y(g(t))) = 0. An oscillation criterion for the above equation is obtained.     

OSCILLATORY BEHAVIOR OF HIGHER ORDER NONLINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

ＯＳＣＩＬＬＡＴＯＲＹＢＥＨＡＶＩＯＲＯＦＨＩＧＨＥＲＯＲＤＥＲＮＯＮＬＩＮＥＡＲＮＥＵＴＲＡＬＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＦｅｎｇＹｕｅｃａｉ（冯月才）（ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔ...     

ASYMPTOTIC AND OSCILLATORY BEHAVIOURS OF SOLUTIONS OF THE 1ST ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH SEVERAL DELAY ARGUMENTS

In this paper authors consider a class of the first order nonlinear neutral differential equations with several delay arguments. Sufficient conditions are obtained which ensure that all nonoscillatory solutions tend to zero as t→ ∞. Criteria are established for all solutions to oscillate.     

OSCILLATION OF NONLINEAR IMPULSIVE PARABOLIC DIFFERENTIAL EQUATIONS WITH SEVERAL DELAYS

Introduetion Theory of delpartial differential equations ean be applied to many fields，sueh as to biology，population growth，engineering，elimate model，medieine，eontrol theory and ehemistry.In the last few years，the fundamental theory of Par     

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.     

STABILITY OF SOLUTIONS OF FIRST ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH OSCILLATORY COEFFICIENTS

ＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＳＯＦＦＩＲＳＴＯＲＤＥＲＮＯＮＬＩＮＥＡＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＯＳＣＩＬＬＡＴＯＲＹＣＯＥＦＦＩＣＩＥＮＴＳ￥ＷａｎｇＱｉｒｕ(王其如）（ＬｕｏｙａｎｇＴｅａｃｈｅｒ?..     

OSCILLATION THEOREM TO SYSTEMS OF IMPULSIVE NEUTRAL DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

In this paper,we study the oscillation of solutions to the systems of impul- sive neutral delay parabolic partial differential equations.Under two different boundary conditions,we obtain some sufficient conditions for oscillation of all solutions to the systems.     

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DELAY

In this paper, by making use of the integral method and some results of the functional differential equations, oscillatory properties of the solutions of certain parabolic partial differential equations with multi-delays are investigated and a series of necessary and sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by the delay and hence reveal the varied difference between these equations and those without delay.     

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY

ＯＳＣＩＬＬＡＴＯＲＹＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＦＩＲＳＴＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＰＩＥＣＥＷＩＳＥＣＯＮＳＴＡＮＴＤＥＬＡＹＦｅｎｇＹｕｅｃａｉ(冯月才）（ＳｏｕｔｈＣｈｉｎ?..     

k-STABILITY OF NONLINEAR NEUTRAL DELAY SYSTEMS

In this paper,we first introduce the concept of k-globally asymptotic stabi- lity and present a differential-difference inequality with infinite delay.By com- bining nonlinear inequality and nonlinear variation-of-parameters formula,we derive the k-globally asymptotic stability criteria for nonlinear neutral system with infinite delay.In the end of this paper,an example is given to illustrate our theory.     

OSCILLATION OF NONLINEAR DELAY DIFFERENCE EQUATIONS

This paper deals with the oscillatory properties of a class of nonlinear difference equations with several delays. Sufficient criteria in the form of infinite sum for the equations to be oscillatory are obtained.     

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY

The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.     

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

1IntroductionThispaperisconcernedwithpositivesolutionOfthesemilinearheatequationswithlocalizedreactionssubjecttoeitherinitialconditions(Cauchyproblem)ortheinitialandboundary-value(DirichletorNeumanntype)conditionswherenisaboundeddomaininRe,icEO.Equations(1.1)canbethoughtofasamodeltodescribesomephysicalphenomena(heatpropagation,chemicalreaction)inwhichthenonlinearreactionsinadynndcalsystemtakesplaceonlyatasinglesite.InthesequelforconvenienceweshallsamplycalltheCauchy,initial-Direchlet,orini…     

OSCILLATIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS——GENERAL LINEARIZED OSCILLA TIONS RESULTS

It is shown that for a wide class of the scalar and vector functional equations of the delay and the neutral type a positive solution exists if and only if the linearized approximating equations are non-oscillatory or, equivalently, the characteristic equations of these linear equations have a real root.     

MONOTONE ITERATIVE TECHNIQUE FOR NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

1Introductiondescently,themonotoneiteratiyetechniqueissuccessfultoprovetheexistenceofextremalsolutionsofvariousnonlinearproblemforordinarydifferentialequations,delaydifferentialequations,integro-differentialequationsetc.,see[1--101.Inthispapertweshallconsidertheexistenceofextremalsolutionsoftheinitialvalueproblem(IVPforshort)fornonlinearneutraldelaydifferentialequationswherefEC[IOxRxRxR,R],CO=C[[--a,0],R],IO=[to,to T],to20,T>0,a<0,T<0,--a=adn{a,T},I=f--a,0]andforanyteIO,u(t s)ECO,sE…     

OSCILLATION THEOREMS FOR SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇｚｈｏｎｇ（靳明忠）（ＷｕｈａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ）Ａｂｓｔｒａｃｔ：Ｓｏｍ...     

QUADRATIC INTEGRABILITY AND BOUNDEDNESS OF THE SOLUTIONS FOR SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

In this paper, by means of auxiliary functions and inequalities, we obtain some sufficient conditions of second order nonhomogeneous delay differential equation belonging to the L.S. or L.S. ∩L.C..     

OSCILLATORY CRITERIA OF SECOND ORDER MATRIX DIFFERENTIAL SYSTEMS

By using a generalized Riccati transformation, we establish some new oscillation criteria which improve and generalize some known criteria in literatures.     

OSCILLATION OF A CLASS OF PARABOLIC PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we investigate the oscillatory property of the solutions of a class or parabonc partial functional differential equations with continuous distrbuted deviating arguments.