SEVERAL CLASSES OF INTEGRABLE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(Ⅰ)FIRST-ORDER EQUATIONS

In this paper we give some results of integrability and several classes of integrableequations of first-order nonlinear ordinary differential equations.Many known results ofintegrability and integrable equations are special cases of them.They may be applied inphysics and mechanics,and to derive soliton equations and find soliton solutions.     

SEVERAL CLASSES OF INTEGRABLE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(Ⅱ)—HIGHER-ORDER EQUATIONS

In this paper,several classes of integrable nonlinear higher-order ordinary differentialequations are given.It is pointed out that some known results of integrability or integrableequations are all special cases of them.These equations have a wide-ranging appliedbackground in physics and mechanics.     

SEVERAL CLASSES OF INTEGRABLE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(Ⅱ)—HIGHER-ORDER EQUATIONS

In this paper, several classes of integrable nonlinear higher-order ordinary differential equations are given. It is pointed out that some known results of integrability or integrable equations are all special cases of them. These equations have a wide-ranging applied background in physics and mechanics.     

ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.     

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

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

THE ASYMPTOTIC EXPRESSION OF THE SOLUTION OF THE CAUCHY’S PROBLEM FOR A HIGHER ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION WHEN THE LIMIT EQUATION HAS SINGULARITY

ＴＨＥＡＳＹＭＰＴＯＴＩＣＥＸＰＲＥＳＳＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮＯＦＴＨＥＣＡＵＣＨＹ’ＳＰＲＯＢＬＥＭＦＯＲＡＨＩＧＨＥＲＯＲＤＥＲＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＨＥＮＴＨＥＬＩＭＩＴＥＱＵＡＴＩＯＮ...     

NUMERICAL SOLUTION OF QUASILINEAR SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION WITHOUT TURNING POINTS

In this paper we consider a quasilinear second order ordinary differential equation equation witha small parameter e.Firstly an approximate problem is constructed.Then an iterativeprocedure is developed.Finally we give an algorithm whose accuracy is good for arbitraryε>0.     

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 SOLUTIONS OF THREE－POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FOURTH ORDER DIFFERENTIAL EQUATION

ＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＯＦＴＨＲＥＥ－ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＦＯＵＲＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ￥ＧａｏＹｏｎｇｘｉｎ（高永馨）（Ｄｅｐａｒｔｍｅｎｔｏ...     

THE FINITE ELEMENT SCHEME FOR ORDINARY DIFFERENTIAL EQUATION WITH SMALL PARAMETER

In this short paper the author has constructed a speical finiteelement scheme and investigated the convergence of this scheme.     

Numerical solution of nonlinear ordinary differential equation for a turning point problem

By using the method in[3],several useful estimations of the derivatives of the solutionof the boundary value problem for a nonlinear ordinary differential equation with a turningpoint are obtained.With the help of the technique in[4],the uniform convergence on thesmall parameterεfor a difference scheme is proved.At the end of this paper,a numericalexample is given.The numerical result coincides with theoretical analysis.     

Instability of solution for a class of the third order nonlinear differential equation

ＩＮＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＴＨＥＴＨＩＲＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＬｕＤｅｙｕａｎ卢德渊（ＲｅｃｅｉｖｅｄＮｏｖ１０１９９４ＣｏｍｍｕｎｉｃａｔｅｄｂｙＺｈａｎｇＳｈｉ...     

Integrable types of nonlinear ordinary differential equations of higher-orders

In this paper some integrable types of more general nonlinear ordinary differentialequations of higher-orders are proposed in virtue of Leibnitz formula,and formulas ofhigher-order derivatives of the composite functions as well as substitution vartables.Theexpressions for the general integrations of some of the equations are presented.The resultsobtained are the generalization of those in the references.Finally,some examples are alsogiven.     

Differentiator series solution of linear differential ordinary equation

１Ｄｉｆｅｒｅｎｔｉａｔｏｒ,ＩｎｖｅｒｓＯｐｅｒａｔｏｒａｎｄＴｈｅｉｒＰｒｏｐｅｒｔｉｅｓ１．１ＤｉｆｅｒｅｎｔｉａｔｏｒａｎｄｉｎｖｅｒｓｏｐｅｒａｔｏｒＳｕｐｐｏｓｅｔｈｅｌｉｎｅａｒｏｒｄｉｎａｒｙｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆ...     

Kink wave determined by parabola solution of a nonlinear ordinary differential equation

By finding a parabola solution connecting two equilibrium points of a planar dynamical system,the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown.Some exact explicit parametric representations of kink wave solutions are given.Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.     

Oscillation theorems of higher order nonlinear delay differential equations

ＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＯＦＨＩＧＨＥＲＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇ－ｚｈｏｎｇ（靳明忠）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＣｏｕｒｓｅｓ,ＹｕｎｎａｎＩｎｓｔｉｔｕｔ...     

Oscillation criteria for second order nonlinear differential equation with damping

1IntroductionandProblem Thefollowingisthesecondordernonlineardifferentialequationwithdamping: [p(t)ψ(y)u(y′)]′ r(t)y′(t) q(t)f(y)g(y′)=0(t≥t0),(1) inwhich,p(t)∈C′([t0,∞),(0,∞)),r(t)∈C([t0,∞),(-∞,∞)),q(t)∈C([t0, ∞),[0,∞))withtheexistenceofT≥t0,q(t)≠0,t∈[T,∞),f(y),g(y),ψ(y),u(y) ∈C((-∞,∞),(-∞,∞)),andyf(y)>0,yu(y)>0,y≠0. Thesolutiony(t)ofEq.(1)iscallednormalsolutionify(t)isthenon_constantsolutionof Eq.(1)andsupt≥t0｜y(t)｜>0(refertoRef.[1]).Anormalsolutionisoscill…     

Two types of new algorithms for finding explicit analytical solutions of nonlinear differential equations

ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｓｅｖｅｒａｌｈｕｎｄｒｅｄｙｅａｒｓ,ｉｔｈａｓｂｅｅｎｂｏｔｈｉｍｐｏｒｔａｎｔａｎｄｄｉｆｆｉｃｕｌｔｐｒｏｊｅｃｔｔｏｃｏｎｓｔｒｕｃｔｔｈｅａｎａｌｙｔｉｃａｌｓｏｌｕｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｍａｎｙｍａｔｈｅｍａｔｉｃｉａｎｓａｎｄｔｈｅｏｒｅｔｉｃａｌｐｈｙｓｉｃｉｓｔｓｈａｖｅｄｏｎｅａｌｏｔｏｆｗｏｒｋ[1～ 5 ].Ｈｏｗｅｖｅｒ,ｔｈｅｒｅｅｘｉｓｔｌｏｔｓｏｆｉｍｐｏｒｔａｎｔａｎｄｂｅｉｎｇｏｆｐ…     

STUDYING THE FOCAL VALUE OF ORDINARY DIFFERENTIAL EQUATIONS BY NORMAL FORM THEORY

ＳＴＵＤＹＩＮＧＴＨＥＦＯＣＡＬＶＡＬＵＥＯＦＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＢＹＮＯＲＭＡＬＦＯＲＭＴＨＥＯＲＹＺｈａｎｇＱｉｃｈａｎｇ（张琪昌）（ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙ．Ｔｉａｎｊｉｎ３０００７２．Ｐ．Ｒ．Ｃ...