This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are ...This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.展开更多
In this paper, we prove existence and multiplicities of solutions for asymptotically linear ordinary differential equations satisfying Sturm-Liouville boundary value conditions with resonance. Adding assumption H3 tha...In this paper, we prove existence and multiplicities of solutions for asymptotically linear ordinary differential equations satisfying Sturm-Liouville boundary value conditions with resonance. Adding assumption H3 that is similar to (LL) in Theorem 1.1, by index theory and Morse theory, we obtain more nontrivial solutions.展开更多
This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix ...This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.展开更多
In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential d...In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge.展开更多
In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the origi...In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.展开更多
In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part,...In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.展开更多
In this paper, we used an interpolation function to derive a Numerical Integrator that can be used for solving first order Initial Value Problems in Ordinary Differential Equation. The numerical quality of the Integra...In this paper, we used an interpolation function to derive a Numerical Integrator that can be used for solving first order Initial Value Problems in Ordinary Differential Equation. The numerical quality of the Integrator has been analyzed to authenticate the reliability of the new method. The numerical test showed that the finite difference methods developed possess the same monotonic properties with the analytic solution of the sampled Initial Value Problems.展开更多
The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanic...The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.展开更多
This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general solutions.In particular,let F(y,w)=0 be a rational algebraic curve over C...This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general solutions.In particular,let F(y,w)=0 be a rational algebraic curve over C.The authors give necessary and sufficient conditions for the autonomous first-order AODE F(y,y′)=0 to have a Liouvillian solution over C.Moreover,the authors show that a Liouvillian solutionαof this equation is either an algebraic function over C(x)or an algebraic function over C(exp(ax)).As a byproduct,these results lead to an algorithm for determining a Liouvillian general solution of an autonomous AODE of order one of genus zero.Rational parametrizations of rational algebraic curves play an important role on this method.展开更多
The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients.We derive estimates for the partial sums and products of the zeros of solutions to th...The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients.We derive estimates for the partial sums and products of the zeros of solutions to the considered equations.These estimates give us bounds for the function counting the zeros of solutions and information about the zero-free domains.展开更多
文摘This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.
文摘In this paper, we prove existence and multiplicities of solutions for asymptotically linear ordinary differential equations satisfying Sturm-Liouville boundary value conditions with resonance. Adding assumption H3 that is similar to (LL) in Theorem 1.1, by index theory and Morse theory, we obtain more nontrivial solutions.
文摘This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.
文摘In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge.
文摘In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.
基金Provincial Science and Technology Foundation of Guizhou
文摘In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.
文摘In this paper, we used an interpolation function to derive a Numerical Integrator that can be used for solving first order Initial Value Problems in Ordinary Differential Equation. The numerical quality of the Integrator has been analyzed to authenticate the reliability of the new method. The numerical test showed that the finite difference methods developed possess the same monotonic properties with the analytic solution of the sampled Initial Value Problems.
文摘The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.
基金supported by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant No.101.04-2017.312。
文摘This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general solutions.In particular,let F(y,w)=0 be a rational algebraic curve over C.The authors give necessary and sufficient conditions for the autonomous first-order AODE F(y,y′)=0 to have a Liouvillian solution over C.Moreover,the authors show that a Liouvillian solutionαof this equation is either an algebraic function over C(x)or an algebraic function over C(exp(ax)).As a byproduct,these results lead to an algorithm for determining a Liouvillian general solution of an autonomous AODE of order one of genus zero.Rational parametrizations of rational algebraic curves play an important role on this method.
文摘The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients.We derive estimates for the partial sums and products of the zeros of solutions to the considered equations.These estimates give us bounds for the function counting the zeros of solutions and information about the zero-free domains.