we consider the third-order neutral functional differential equations with deviating arguments. A new theorem is presented that improves a number of results reported in the literature. Examples are included to illustr...we consider the third-order neutral functional differential equations with deviating arguments. A new theorem is presented that improves a number of results reported in the literature. Examples are included to illustrate new results.展开更多
In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and imp...In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and improve many known oscillation criteria because the article just generalizes Meng and Xu’s results.展开更多
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
Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equ...Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.展开更多
In this paper, we obtained some sufficient conditions for the oscillation of all solutions of the second order neutral differential equation of the form where , and . Examples are provided to illustrate the main results.
Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case whe...Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case where former results can not be applied in this paper.展开更多
In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
By an associate linear equation, we obtain a linearized oscillation result of certain odd-order nonlinear neutral delay differential equation. The result answers partially an open problem proposed by Gyori and Ladas.
Consider the nonlinear neutral delay differential equationwhere P, Q ∈ C([t0,∞),R), τ > 0, δ > 0. We obtain a linearized oscillation result by an associate linear equation in the case when liminfP(t) = p0 ∈...Consider the nonlinear neutral delay differential equationwhere P, Q ∈ C([t0,∞),R), τ > 0, δ > 0. We obtain a linearized oscillation result by an associate linear equation in the case when liminfP(t) = p0 ∈[-1,0).展开更多
This peper discusses a class of second order nonlinear neutral differential equations with variable coefficients and variable d eviations. Oscillation oriterta for all solutions of the equations are estublished and su...This peper discusses a class of second order nonlinear neutral differential equations with variable coefficients and variable d eviations. Oscillation oriterta for all solutions of the equations are estublished and sufficient conditions are also given to ensure those derivatives of all differentiable solutions of the equations to be oscillatory.展开更多
By introducing two integral operators and using the integral averaging technique, some new oscillation criteria are obtained for a class of high order neutral differential equation with continuous deviating arguments....By introducing two integral operators and using the integral averaging technique, some new oscillation criteria are obtained for a class of high order neutral differential equation with continuous deviating arguments. These results are different from most known ones in the sense that they depend on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line.展开更多
Some new oscillation theorems for a second order superlinear-sublinear neutral differential equation are established under some conditions. Our results improve and extend the main results in the previous literature. E...Some new oscillation theorems for a second order superlinear-sublinear neutral differential equation are established under some conditions. Our results improve and extend the main results in the previous literature. Explicit examples related to the main results are given.展开更多
We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equat...We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.展开更多
First we establish the equivalence of the oscillation of the following two dif- ferential equations and (r(t)y'(t))' + τ^(-1)f(t, r(t -σ1(t))y(t),..., r(t -σn(t))y(t)) = 0. (**) Next, we establish the neces...First we establish the equivalence of the oscillation of the following two dif- ferential equations and (r(t)y'(t))' + τ^(-1)f(t, r(t -σ1(t))y(t),..., r(t -σn(t))y(t)) = 0. (**) Next, we establish the necessary and sufficient conditions of all solutions to (*) being oscillatory, when f is strongly superlinear or strongly sublinear.展开更多
We obtain sufficient conditions for the oscillation of all solutions of the neutral equationOur results extend and improve some recent results in literature. Some examples are also given which can be investigated succ...We obtain sufficient conditions for the oscillation of all solutions of the neutral equationOur results extend and improve some recent results in literature. Some examples are also given which can be investigated successfully using our results but cannot be handled by any previous techniques or results.展开更多
In this paper, we prove that, under appropriate hypotheses, the odd-order nonlinear neutral delay differential equation has the same oscillatory character as the associated linear equation with periodic coefficients O...In this paper, we prove that, under appropriate hypotheses, the odd-order nonlinear neutral delay differential equation has the same oscillatory character as the associated linear equation with periodic coefficients Our method is based on the establishment of a new comparison theorem for the oscillation of Eq.(E). Hence we prove that the parameter set such that Eq.(E) has a nonoscillatory solution is closed in certain metric space, and avoid the difficulty to set the necessary and sufficient condition for the oscillation of Eq.(E).展开更多
A new oscillation result is established for the first order neutral differential equationx(t) - px(t - (?)) + qx(t - σ) = 0.The results extends and improves some existing results in the literature.
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
Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous ...Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.展开更多
文摘we consider the third-order neutral functional differential equations with deviating arguments. A new theorem is presented that improves a number of results reported in the literature. Examples are included to illustrate new results.
文摘In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and improve many known oscillation criteria because the article just generalizes Meng and Xu’s results.
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 the NSF of Guangdong Province(S2011010004447,S2012040006865)
文摘Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.
文摘In this paper, we obtained some sufficient conditions for the oscillation of all solutions of the second order neutral differential equation of the form where , and . Examples are provided to illustrate the main results.
文摘Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case where former results can not be applied in this paper.
文摘In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
基金This work is supported by the NNSF of China (No. 10071018).
文摘By an associate linear equation, we obtain a linearized oscillation result of certain odd-order nonlinear neutral delay differential equation. The result answers partially an open problem proposed by Gyori and Ladas.
基金This work is supported by the NNSF of China(No.10071018).
文摘Consider the nonlinear neutral delay differential equationwhere P, Q ∈ C([t0,∞),R), τ > 0, δ > 0. We obtain a linearized oscillation result by an associate linear equation in the case when liminfP(t) = p0 ∈[-1,0).
文摘This peper discusses a class of second order nonlinear neutral differential equations with variable coefficients and variable d eviations. Oscillation oriterta for all solutions of the equations are estublished and sufficient conditions are also given to ensure those derivatives of all differentiable solutions of the equations to be oscillatory.
基金Supported by the NSF of Hebei Province and the NSF of Hebei Institute of Architecture and Civil Engineering.
文摘By introducing two integral operators and using the integral averaging technique, some new oscillation criteria are obtained for a class of high order neutral differential equation with continuous deviating arguments. These results are different from most known ones in the sense that they depend on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line.
基金supported by the NSF of Guangdong Province(Nos.S2012040006865and S2013010013050)the Science Education"The Twelfth Five Year Plan"2013 Year Project of Guangdong Province(No.2013JK128)the Natural Science Foundation of Guangdong University of Education(No.2014yjxm05)
文摘Some new oscillation theorems for a second order superlinear-sublinear neutral differential equation are established under some conditions. Our results improve and extend the main results in the previous literature. Explicit examples related to the main results are given.
文摘We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.
文摘First we establish the equivalence of the oscillation of the following two dif- ferential equations and (r(t)y'(t))' + τ^(-1)f(t, r(t -σ1(t))y(t),..., r(t -σn(t))y(t)) = 0. (**) Next, we establish the necessary and sufficient conditions of all solutions to (*) being oscillatory, when f is strongly superlinear or strongly sublinear.
文摘We obtain sufficient conditions for the oscillation of all solutions of the neutral equationOur results extend and improve some recent results in literature. Some examples are also given which can be investigated successfully using our results but cannot be handled by any previous techniques or results.
文摘In this paper, we prove that, under appropriate hypotheses, the odd-order nonlinear neutral delay differential equation has the same oscillatory character as the associated linear equation with periodic coefficients Our method is based on the establishment of a new comparison theorem for the oscillation of Eq.(E). Hence we prove that the parameter set such that Eq.(E) has a nonoscillatory solution is closed in certain metric space, and avoid the difficulty to set the necessary and sufficient condition for the oscillation of Eq.(E).
基金Supported by the Education Department of Hainan Province (HjKj200317).
文摘A new oscillation result is established for the first order neutral differential equationx(t) - px(t - (?)) + qx(t - σ) = 0.The results extends and improves some existing results in the literature.
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
文摘Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.
