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.
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
In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)...In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.展开更多
By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral dela...By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.展开更多
In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and D...In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet＇s boundary value conditions.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
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
Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is imp...Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.展开更多
In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differen...In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained.展开更多
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
This paper has given necessary and sufficient conditions for oscillation of a classof higher order nonlinear delay differential equations, and given some sufficientconditions or necessary conditions for oscillation of...This paper has given necessary and sufficient conditions for oscillation of a classof higher order nonlinear delay differential equations, and given some sufficientconditions or necessary conditions for oscillation of a forced delay differentialequation.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
Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and ...Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.展开更多
The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging techniq...The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging technique. Some well known results in the literature are extended. Moreover, two examples are given to illustrate the theoretical analysis.展开更多
This paper discusses a class of second order nonlinear differential euqations. By using the generalized Riccati technique and the averaging technique, some new oscillation criteria are obtained.
The main desire of this paper is to present several new interval oscillation criteria related to a generalized Riccati technique for certain second-order nonlinear differential equations.Our results extend some known ...The main desire of this paper is to present several new interval oscillation criteria related to a generalized Riccati technique for certain second-order nonlinear differential equations.Our results extend some known equations.Finally,several examples illustrate the effectiveness of our results.展开更多
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
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
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
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.
文摘In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.
文摘By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.
基金the Natural Science Foundation of Hunan Province(10471086)the Science Research Foundation of Administration of Education of Hunan Province(07C164)
文摘In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet＇s boundary value conditions.
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.
文摘Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.
基金Supported by the Natural Science Foundation of China(10471086)Supported by the Science Research Foundation of Department of Education of Hunan Province(07C164)
文摘In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained.
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
文摘This paper has given necessary and sufficient conditions for oscillation of a classof higher order nonlinear delay differential equations, and given some sufficientconditions or necessary conditions for oscillation of a forced delay differentialequation.
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Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.
文摘The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging technique. Some well known results in the literature are extended. Moreover, two examples are given to illustrate the theoretical analysis.
文摘This paper discusses a class of second order nonlinear differential euqations. By using the generalized Riccati technique and the averaging technique, some new oscillation criteria are obtained.
基金Supported by Science Foundation for Young Teachers of Northeast Normal University（20080105） Supported by NSFC（10926105+2 种基金1100104110971022） Supported by SRFDP（200802001008）
文摘The main desire of this paper is to present several new interval oscillation criteria related to a generalized Riccati technique for certain second-order nonlinear differential equations.Our results extend some known equations.Finally,several examples illustrate the effectiveness of our results.
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
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.
