Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect...This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.展开更多
In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish...In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.展开更多
In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of perio...In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.展开更多
This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether me...This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether method and the Poisson method. Then the solution of the higher-order equation can be obtained by integrating the solution of the second-order equation.展开更多
We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such ...We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and展开更多
In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating argum...In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.展开更多
The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases： ε/μ^...The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases： ε/μ^2→0 （μ →0）, μ^2/ε →0 （ε → 0） andε = μ^2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.展开更多
In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see add...In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see additive extrapolation method before. This new method has a great advantage over additive extrapolation method because it keeps group property. If this method is used to construct higher order schemes from lower symplectic schemes, the higher order ones are also symplectic. First we introduce the concept of adjoint methods and some of their properties. We show that there is a self-adjoint scheme corresponding to every method. With this self-adjoint scheme of lower order, we can construct higher order schemes by multiplicative extrapolation method, which can be used to construct even much higher order schemes. Obviously this constructing process can be continued to get methods of arbitrary even order.展开更多
The existence of positive solution is proved for a （k, n - k） conjugate boundary value problem in which the nonlinearity may make negative values and may be singular with respect to the time variable. The main resul...The existence of positive solution is proved for a （k, n - k） conjugate boundary value problem in which the nonlinearity may make negative values and may be singular with respect to the time variable. The main results of Agarwal et al. （Agarwal R P, Grace S R, O＇Regan D. Semipositive higher-order differential equations. Appl. Math. Letters, 2004, 14： 201-207） are extended. The basic tools are the Hammerstein integral equation and the Krasnosel＇skii＇s cone expansion-compression technique.展开更多
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
基金supported by the National Natural Science Foundation of China (11101096)
文摘This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.
文摘In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.
基金Supported by the Natural Science Foundation of Guangdong Province (No.9151063301000008)
文摘In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.
基金Project supported by the National Natural Science Foundation of China(Grant No10572021)Doctoral Programme Foundation of Institution of Higher Education of China(Grant No20040007022)
文摘This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether method and the Poisson method. Then the solution of the higher-order equation can be obtained by integrating the solution of the second-order equation.
基金This research is supported by NNSF of China(19875083,10275032).
文摘We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and
基金Natural Science Foundation of Anhui Province (050460103)the Key Natural Science Foundation by the Bureau of Education of Anhui Province(KJ2008A05ZC).
文摘In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.
文摘The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases： ε/μ^2→0 （μ →0）, μ^2/ε →0 （ε → 0） andε = μ^2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.
文摘In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see additive extrapolation method before. This new method has a great advantage over additive extrapolation method because it keeps group property. If this method is used to construct higher order schemes from lower symplectic schemes, the higher order ones are also symplectic. First we introduce the concept of adjoint methods and some of their properties. We show that there is a self-adjoint scheme corresponding to every method. With this self-adjoint scheme of lower order, we can construct higher order schemes by multiplicative extrapolation method, which can be used to construct even much higher order schemes. Obviously this constructing process can be continued to get methods of arbitrary even order.
文摘The existence of positive solution is proved for a （k, n - k） conjugate boundary value problem in which the nonlinearity may make negative values and may be singular with respect to the time variable. The main results of Agarwal et al. （Agarwal R P, Grace S R, O＇Regan D. Semipositive higher-order differential equations. Appl. Math. Letters, 2004, 14： 201-207） are extended. The basic tools are the Hammerstein integral equation and the Krasnosel＇skii＇s cone expansion-compression technique.
