共查询到20条相似文献,搜索用时 15 毫秒
1.
On the reflecting function and the qualitative behavior of solutions of some non-autonomous differential equations
下载免费PDF全文
![点击此处可从《Journal of Applied Analysis & Computation》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Zhengxin Zhou 《Journal of Applied Analysis & Computation》2017,7(2):523-531
In this article, we use the Mironenko''s method to discuss the qualitative behavior of some non-autonomous differential equations. We study the structure of the reflecting functions of the simplest differential equations, and obtain some sufficient conditions under which these equations have the rational reflecting functions. We apply the obtained results to discuss the numbers of periodic solutions of the non-autonomous differential systems and derive some sufficient conditions for a critical point of theirs to be a center. 相似文献
2.
On the equivalence of two differential equations by means of reflecting functions coinciding
下载免费PDF全文
![点击此处可从《Journal of Applied Analysis & Computation》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this article, we discuss the equivalence of two differential systems by using the method of reflecting functions. We obtain some necessary and sufficient conditions under which certain differential equations are equivalent. Given these results, new types of differential systems equivalent to the given systems can be found. We also discussed the qualitative behavior of the periodic solutions of such differential systems. These results are new, in the sense that they generalize previous discussions on the equivalence of differential systems. 相似文献
3.
zhengxin zhou Richang Tai Fei Wang Shuying Zong 《Journal of Applied Analysis & Computation》2014,4(1):103-114
In this article we use the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Riccati equation and some polynomial differential equations. The results are applied to discussion of the qualitative behavior of periodic solutions of these complicated differential equations. 相似文献
4.
OSCILLATIONSOFFIRSTORDERNONLINEARRETARDEDDIFFERENTIALEQUATIONS¥WangQiru(王其如)(LuoyangTeachers'College,洛阳师范高等专科学校,邮编:471022)Abs... 相似文献
5.
ON THE EQUIVALENCE OF THE ABEL EQUATION 总被引:2,自引:0,他引:2
This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations. 相似文献
6.
G. A. Chumakov 《Siberian Mathematical Journal》2007,48(5):949-960
This is a qualitative analysis of a system of two nonlinear ordinary differential equations which arises in modeling the self-oscillations of the rate of heterogeneous catalytic reaction. The kinetic model under study accounts for the influence of the reaction environment on the catalyst; namely, we consider the reaction rate constant to be an exponential function of the surface concentration of oxygen with an exponent μ. We study the necessary and sufficient conditions for the existence of periodic solutions of differential equations as depending on μ. We formulate some sufficient conditions for all trajectories to converge to a steady state and study global behavior of the stable manifolds of singular saddle points. 相似文献
7.
In this work, the asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses is investigated. By impulsive differential inequality and Riccati transformation, sufficient conditions of asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses are obtained. An example is also inserted to illustrate the impulsive effect. 相似文献
8.
Jurang Yan 《Journal of Mathematical Analysis and Applications》2002,265(2):332-342
The oscillatory and asymptotic behavior of first-order nonlinear delay impulsive differential equations and inequalities is studied. Some new sharp sufficient conditions for oscillation and nonoscillation of solutions of the equations and inequalities are obtained. Many known results are improved. In particular, the conditions are necessary and sufficient if the equations and inequalities are autonomous. 相似文献
9.
This paper has made researches on first order neutral differential equations with variable coefficients and several deviations. The asymptotic behavior of nonoscillatory solutions of the equations are discussed. Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained. The relevent results in [1—3] are improved and generalized . 相似文献
10.
《Applied Mathematics Letters》2001,14(7):825-830
Classification schemes for positive solutions of a class of higher-order nonlinear functional differential equations are given in terms of their asymptotic behavior, and necessary as well as sufficient conditions for the existence of these solutions are also provided. 相似文献
11.
12.
13.
We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument. 相似文献
14.
We consider a family of integral equations used as models of some living systems. We prove that an integral equation is reducible to the equivalent Cauchy problem for a non-autonomous differential equation with point or distributed delay dependently on the choice of the survival function of system elements. We also study the issues of the existence, uniqueness, nonnegativity, and continuability of solutions. We describe all stationary solutions and obtain sufficient conditions for their asymptotic stability. We have found sufficient conditions for the existence of a limit of solutions on infinity and present an example of equations where the rate of generation of elements of living systems is described by a unimodal function (namely, the Hill function). 相似文献
15.
结合微分方程理论和函数空间理论,研究了单位圆上一类特殊高阶线性微分方程解的性质,得到当方程系数满足某些条件时,其解属于某类函数空间的充分条件. 相似文献
16.
This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with
quasiderivatives. We give the necessary and sufficient conditions guaranteeing the existence of bounded nonoscillatory solutions.
Sufficient conditions are proved via a topological approach based on the Banach fixed point theorem. 相似文献
17.
高阶泛函微分方程的振动性质* 总被引:11,自引:0,他引:11
本文借助于Lebesgue测度等工具研究了一类高阶非线性泛函微分方程的振动性质.文中指出.在一定条件下,方程的非振动解仅有两类,而且给出了每一类非振动解存在的必要条件,同时也建立了方程振动的若干充分判据. 相似文献
18.
19.
Jian Zhou 《Applied mathematics and computation》2011,218(7):3144-3148
Using reflecting function, we give the conditions under which some complex differential systems are equivalent to the relatively simple differential system. The obtained results are applied to study the behavior of solutions of these complex differential systems. 相似文献
20.
Yuexin Yan Yingxin Pan Feifei Lu Zhengxin Zhou 《Journal of Nonlinear Modeling and Analysis》2019,1(2):207-220
In this paper, first of all we give the necessary and sufficient con-
ditions of the center of a class of planar quintic differential systems by using
reflecting function method, and provide a simple proof of this results. Sec-
ondly, We use the reflecting integral to research the equivalence of the Abel
equation and some complicated equations and derive their center conditions
and discuss their integrability. 相似文献