Consider the neutral equation with variable coefficients dt[x(t) - P(t)x(t - γ)] + Q(t)x(t -σ) =0where P,Q∈C[[t0,,∞),R+] and σ,∈R+. We obtain some new sufficient conditions for the oscillation of soutions of the...Consider the neutral equation with variable coefficients dt[x(t) - P(t)x(t - γ)] + Q(t)x(t -σ) =0where P,Q∈C[[t0,,∞),R+] and σ,∈R+. We obtain some new sufficient conditions for the oscillation of soutions of the.abave equation without the restriction:0 P(t) 1 or P(t) 1.展开更多
Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
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
The oscillations of the advanced difference equationsxn - xn-1 - p(n)xn+k = 0, n ≥ 0, (*)andXn - Xn-1 - ∑i=1mpi(n)xn+ki=0, n ≥0, (**)are investigated, where p(n),pi(n)(i = 1,2,..., m)...The oscillations of the advanced difference equationsxn - xn-1 - p(n)xn+k = 0, n ≥ 0, (*)andXn - Xn-1 - ∑i=1mpi(n)xn+ki=0, n ≥0, (**)are investigated, where p(n),pi(n)(i = 1,2,..., m) are nonnegative real numbers. First. a sufficienet condition for the oscillation of equation (*) is obtained, then the result is generalized to the equation (**). At last, an example is given to illustrate the advantages of our results. Our results are new.展开更多
： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati tech...： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
Consider the neutral differential equations with variable coefficients and delays [x(t)-p(t)x(t-r(t))]'+ Qj(t)x(t-σj(t))=0. (1)We establish sufficient conditions for the oscillation of equation (1). Our condition...Consider the neutral differential equations with variable coefficients and delays [x(t)-p(t)x(t-r(t))]'+ Qj(t)x(t-σj(t))=0. (1)We establish sufficient conditions for the oscillation of equation (1). Our condition is 'sharp' in the sense that when all the coefficients and delays of the equation are constants.Our conclusions improve and generalize some known results.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
In this paper, we are concerned with the second order neutral difference equation with continuous variable. Using the integral transformation and generalized Riccati transformation, we obtain some oscillation criteria.
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.
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
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
文摘Consider the neutral equation with variable coefficients dt[x(t) - P(t)x(t - γ)] + Q(t)x(t -σ) =0where P,Q∈C[[t0,,∞),R+] and σ,∈R+. We obtain some new sufficient conditions for the oscillation of soutions of the.abave equation without the restriction:0 P(t) 1 or P(t) 1.
文摘Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
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Project supported by NNSFC (No.10071022), Mathematical Tianyuan Foundation of China (No.TY10026002-01-05-03) and Shanghai Priority Academic Discipline.
文摘The oscillations of the advanced difference equationsxn - xn-1 - p(n)xn+k = 0, n ≥ 0, (*)andXn - Xn-1 - ∑i=1mpi(n)xn+ki=0, n ≥0, (**)are investigated, where p(n),pi(n)(i = 1,2,..., m) are nonnegative real numbers. First. a sufficienet condition for the oscillation of equation (*) is obtained, then the result is generalized to the equation (**). At last, an example is given to illustrate the advantages of our results. Our results are new.
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)
文摘： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.
文摘Consider the neutral differential equations with variable coefficients and delays [x(t)-p(t)x(t-r(t))]'+ Qj(t)x(t-σj(t))=0. (1)We establish sufficient conditions for the oscillation of equation (1). Our condition is 'sharp' in the sense that when all the coefficients and delays of the equation are constants.Our conclusions improve and generalize some known results.
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.
文摘In this paper, we are concerned with the second order neutral difference equation with continuous variable. Using the integral transformation and generalized Riccati transformation, we obtain some oscillation criteria.
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.
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.
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Supported by the Natural Science Foundation of Hunan Province(12JJ6006)Hunan Province Science and Technology Project(2012FJ3107)the National Natural Science Foundation of China(11071222)
