The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscilla...The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.展开更多
We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish...We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish new oscillatory criteria which include two necessary and sufficient conditions. Moreover, we point out that how the power γ plays its role. Some interesting examples are given to illustrate the versatility of our results.展开更多
A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the ze...A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.展开更多
In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions i...In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.展开更多
In this paper, a new oscillating result is established for the first order neutral delay differential equation with positive and negative coefficients, which improves and generalizes several results in the literatures.
Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison ...Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison criteria obtained in the literature [1] and [2].展开更多
This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' condition...This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.展开更多
Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = ...Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = 1,2, …, n.展开更多
In this paper, we further investigate a class of first order neutral Pantograph differential equations of Euler type by Guan and Shen . Some infinite-integral conditions for the oscillation of all solutions are establ...In this paper, we further investigate a class of first order neutral Pantograph differential equations of Euler type by Guan and Shen . Some infinite-integral conditions for the oscillation of all solutions are established.展开更多
文摘The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.
基金supported by National Natural Science Foundation of China (Grant No. 11271379)Guangzhou Postdoctoral Science Research Foundation Project (Grant No. gdbsh2014003)
文摘We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish new oscillatory criteria which include two necessary and sufficient conditions. Moreover, we point out that how the power γ plays its role. Some interesting examples are given to illustrate the versatility of our results.
基金the Science Foundation of Educational Committee of Hunan Provinc
文摘A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.
基金the National Natural Science Foundation of China(1 0 0 71 0 1 8)
文摘In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.
基金Supported by the NSF Education Dept. (hjkj200317) and the NSF of Hainan Province (80403).
文摘In this paper, a new oscillating result is established for the first order neutral delay differential equation with positive and negative coefficients, which improves and generalizes several results in the literatures.
文摘Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison criteria obtained in the literature [1] and [2].
基金Research supported by National Natural Science Foundation of P. R. China (10071016) by Foundation of the Education Department for Excellent Teacher of University.
文摘This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.
基金Project supported by Scientific Research Fund of Hunan Provincial Education Department (China)(granted 03C427).
文摘Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = 1,2, …, n.
基金supported by Scientific Research Fund of Hengyang Bureau of Science andTechnology (06KJ15)
文摘In this paper, we further investigate a class of first order neutral Pantograph differential equations of Euler type by Guan and Shen . Some infinite-integral conditions for the oscillation of all solutions are established.
