SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS

ＳＩＮＧＵＬＡＲ　ＰＥＲＴＵＲＢＡＴＩＯＮＳ　ＦＯＲ　Ａ　ＣＬＡＳＳ　ＯＦ　ＢＯＵＮＤＡＲＹ　ＶＡＬＵＥ　ＰＲＯＢＬＥＭＳ　ＯＦ　ＨＩＧＨＥＲ　ＯＲＤＥＲ　ＮＯＮＬＩＮＥＡＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＳｈｉＹｕａｎｉｎｇ（史玉明）...     

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS OF SECOND ORDER NONLINEAR EQUATION

ＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＴＷＯＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＳＥＣＯＮＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮ（杨作东）ＥＸＩＳＴＥＮＣＥＯＦＰＯＳ...     

NUMERICAL SIMULATION OF THREE DIMENSIONAL TURBULENT FLOW IN SUDDENLY EXPANDED RECTANGULAR DUCT

ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＴＨＲＥＥＤＩＭＥＮＳＩＯＮＡＬＴＵＲＢＵＬＥＮＴＦＬＯＷＩＮＳＵＤＤＥＮＬＹＥＸＰＡＮＤＥＤＲＥＣＴＡＮＧＵＬＡＲＤＵＣＴＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＴＨＲＥＥＤＩＭＥＮＳＩＯＮＡＬＴＵＲＢＵ...     

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＦＲＯＢＬＥＭＳＯＦＲＥＡＣＴＩＯＮＤＩＦＦＵＳｌＯＮＥＱＵＡＴＩＯＮＷＩＴＨＤＥＬＡＹＺｈａｎｇＸｉａｎｇ（张祥）（ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ｗｕ...     

A UNIFORMLY CONVERGENT DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF A HIGH ORDER ELLIPTIC DIFFERENTIAL EQUATION

ＡＵＮＩＦＯＲＭＬＹＣＯＮＶＥＲＧＥＮＴＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＦＯＲＴＨＥＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭＯＦＡＨＩＧＨＯＲＤＥＲＥＬＬＩＰＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ（刘国庆）（苏煜城）ＡＵＮＩＦＯ...     

EXISTENCE THEOREMS OF SOLUTIONS FOR TWO－POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

ＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＷＯ－ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＳＥＣＯＮＤＯＲＤＥＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺｈａｎｇＳｈｉｓ...     

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

ＡＵＮＩＦＯＲＭＬＹＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭＦＯＲＡＳＥＭＩＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＭＩＸＥＤＢＯＵＮＤＡＲＹＶＡＬＵＥＣＯＮＤＩＴ...     

THE EXISTENCE OF PERIODIC SOLUTION OF THE FOURTH ORDINARY NONLINEAR DIFFERENTIAL EQUATION CAUSED BY FLOW－IN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＦＯＵＲＴＨＯＲＤＩＮＡＲＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＣＡＵＳＥＤＢＹＦＬＯＷ－ＩＮＤＵＣＥＤＶＩＢＲＡＴＩＯＮＧｕＱｉｎｇ－ｆａｎｇ（顾清芳）Ｔａ...     

NUMERICAL SIMULATION OF FLOW OF HIGHLY VISCOELASTIC FLOW IN THREE－DIMENSIONAL VARYING THICK SLIT CHANNEL

（杨伯源）（李勇）ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＦＬＯＷＯＦＨＩＧＨＬＹＶＩＳＣＯＥＬＡＳＴＩＣＦＬＯＷＩＮＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＡＲＹＩＮＧＴＨＩＣＫＳＬＩＴＣＨＡＮＮＥＬ￥ＹａｎｇＢｏｙｕａｎ；ＬｉＹｏｎｇ（Ｄｅｐａｒｔ...     

INITIAL BOUNDARY VALUE PROBLEMS FOR A CLASS OF NONLINEAR INTEGRO－PARTIAL DIFFERENTIAL EQUATIONS

ＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯ－ＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＣｕｉＳｈａｎｇ－ｂｉｎ（崔尚斌）（Ｄｅｐｔ．ｏｆＭａｔｈ．,ＬａｎｚｈｏｕＵｎｉ...     

SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION

IntroductionThereweresomeresultsofstudyingonboundaryvalueproblemsforfunctionaldifferentialequation[1～6 ]byemployingthetoplolgicaldegreetheoryandsomefixedpointprinciplesinrecentyears.Buttheworktostudyboundaryvalueproblemsfordelaydifferentialequationwithsmallparameterbymeansofthetheoryofsingularperturbationrarelyappeared[7～11].Thereasonforitisthattheworktoconstructtheuppersolutionandlowersolutionforthecaseofdifferentialequationwithdelayisdifficult.Theauthorhasstudiedakindofboundaryvalueproblem…     

Oscillation behavior of solutions for even order neutral functional differential equations

Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.     

On global solutions of functional differential equations

We construct a system of linear differential equations all solutions of which are global solutions of a system of functional differential equations. We substantiate the existence of this system and examine some properties of its solutions.     

Problem of periodic solutions for neutral functional differential equation

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＣ(ｋ- 1)2π =ｈ(ｔ) ｜ｈ :Ｒ →Ｒｉｓ (ｋ -1 )＿ｔｈｏｒｄｅｒｃｏｎｔｉｎｕｏｕｓｄｉｆｆｅｒｅｎｔｉａｂｌｅａｎｄｈ(ｔ+ 2π) ≡ｈ(ｔ) ,　　Ｃ2π =ｈ(ｔ) ｜ｈ :Ｒ →Ｒｉｓｃｏｎｔｉｎｕｏｕｓａｎｄｈ(ｔ+ 2π) ≡ｈ(ｔ) ,　　‖ｈ(ｔ)‖ =ｓｕｐｔ∈ [0 ,2π] ｜ｈ(ｔ) ｜ ,　　‖ｈ(ｔ)‖Ｐｋ- 1 =ｍａｘ‖ｈ(ｔ)‖ ,‖ｈ′(ｔ)‖ ,… ,‖ｈ(ｋ- 1) (ｔ)‖ ,　　ｘ(ｍ) (ｔ+ ·) (θ) =ｘ(ｍ) (ｔ+θ)　　θ∈Ｒ (ｍ =0 ,1 ,2 ,… ,ｋ-1 ) .Ｃｌｅａｒｌｙ ,ｘ(ｍ) (ｔ + ·) ∈Ｃ2π, …     

Center Manifold Theory for Functional Differential Equations of Mixed Type

We study the behaviour of solutions to nonlinear autonomous functional differential equations of mixed type in the neighbourhood of an equilibrium. We show that all solutions that remain sufficiently close to an equilibrium can be captured on a finite dimensional invariant center manifold, that inherits the smoothness of the nonlinearity. In addition, we provide a Hopf bifurcation theorem for such equations. We illustrate the application range of our results by discussing an economic life-cycle model that gives rise to functional differential equations of mixed type.     

Hopf Bifurcation for Retarded Functional Differential Equations and for Semiflows in Banach Spaces

We indicate how a Hopf bifurcation theorem for retarded functional differential equations can be proved correctly, following an approach that is described, but not carried out properly in the literature. Then we state and prove a Hopf bifurcation theorem for general semiflows in Banach spaces, using different methods. The general statement includes the case of retarded functional differential equations.     

A structured population model and a related functional differential equation: Global attractors and uniform persistence

A structured population model of a single population having two distinct life stages is considered. The model equations, consisting of a hyperbolic partial differential equation coupled to an ordinary differential equation, can be reduced to a single, scalar functional differential equation. This allows us to use the well-developed dynamical systems theory for functional differential equations in order to study the dynamical system generated by the more complicated coupled system. A precise relation is established between the dynamical systems generated by each system of equations and a correspondence between their respective global attractors is made. The two systems are topologically equivalent on their respective attractors. These relationships are used to determine sharp sufficient conditions for the uniform persistence of the population.     

Exponential Dichotomies,the Fredholm Alternative,and Transverse Homoclinic Orbits in Partial Functional Differential Equations

In this paper we investigate the transversality of homoclinic orbits in partial functional differential equations. We first discuss the exponential dichotomies for linear operator equations. Then we show that the Fredholm Alternative holds if the homogeneous equation has exponential dichotomies on R. Transversality of homoclinic orbits for periodically perturbed partial functional differential equations is studied using the Liapunov-Schmidt method and the Melnikov integral. Ams Subject Classifications: 35R10; 58F14.     

Oscillatory properties of the solutions of nonlinear delay hyperbolic differential equations of neutral type

Ｔｈｅｎｅｗｌｙ—ｄｅｖｅｌｏｐｅｄｔｈｅｏｒｙｏｆｎｏｎｌｉｎｅａｒｄｅｌａｙｐａｒｔｉａｌｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓａｒｅａｐｐｌｉｅｄｉｎｍａｎｙｆｉｅｌｄｓ,ｓｕｃｈａｓｉｎｅｎｇｉｎｅｅｒｉｎｇ ,ｂｉｏｌｏｇｙ,ｍｅｄｉｃｉｎｅ,ｐｈｙｓｉｃｓａｎｄｃｈｅｍｉｓｔｒｙ .Ａｓｅｒｉｅｓｏｆｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓ,ｎｅｃｅｓｓａｒｙａｎｄｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓｆｏｒｏｓｃｉｌｌａｔｉｏｎｓｏｆｔｈｅｅｑｕａｔｉｏｎｓｗｅｒ…     

On Some Extension of Center Manifold Method to Functional Differential Equations with Oscillatory Decreasing Coefficients and Variable Delays

We propose an asymptotic integration method for certain class of functional differential systems. This class includes the delay differential equations with oscillatory decreasing coefficients and variable delays that are close to constants at infinity. Both the ideas of the centre manifold theory and the averaging method together with some classical asymptotic theorems are used to construct the asymptotics for solutions. We illustrate the asymptotic integration method by constructing the asymptotics for solutions of scalar differential equation with variable delay.