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
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
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
This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations,...This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations, and these results are illustrated by some examples.展开更多
Sufficient conditions for the oscillation of the neutral equation d/dt[x(t) - R(t)x(t - r)] + P(t)x(t - r) - Q(t)x(t - δ) = 0,where P,Q,R ∈ C([t0,∞), R+), and r, T, δ ∈ (0,∞), are obtained for the case where for...Sufficient conditions for the oscillation of the neutral equation d/dt[x(t) - R(t)x(t - r)] + P(t)x(t - r) - Q(t)x(t - δ) = 0,where P,Q,R ∈ C([t0,∞), R+), and r, T, δ ∈ (0,∞), are obtained for the case where former results can not be applied.展开更多
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
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
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
The problem of oscillation of neutral delay differential equations is of theoretical as well as practical interest, and the oscillation theory of such equations has been extensively developed during the past few years...The problem of oscillation of neutral delay differential equations is of theoretical as well as practical interest, and the oscillation theory of such equations has been extensively developed during the past few years. However, almost all the known results deal with the equations only with positive coefficients.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
This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such a...This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.展开更多
Oscillation criteria are established for third-order neutral delay differential equations with deviating arguments. These criteria extend and generalize those results in the literature. Moreover, some illustrating exa...Oscillation criteria are established for third-order neutral delay differential equations with deviating arguments. These criteria extend and generalize those results in the literature. Moreover, some illustrating examples are also provided to show the importance of our results.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
In this paper,we study one type of odd-order neutral delay differential equation. Suffcient conditions for the oscillation of every solution to this type of differential equation are given.
Abstract In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.
In this paper, a new sufficient condition for the oscillation of all solutions of first order neutral delay differential equations is obtained. Secondly, the result can also be extended to a general neutral differenti...In this paper, a new sufficient condition for the oscillation of all solutions of first order neutral delay differential equations is obtained. Secondly, the result can also be extended to a general neutral differential equation, and many known results in the literatures are improved.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
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.
Oscillation criteria for the delay differential equationwhere p, T are non-negative real-valued continuous functions are investigated in the case when the numberssatisfy 0 < k < 1/e and 1/e < L < 1. The pr...Oscillation criteria for the delay differential equationwhere p, T are non-negative real-valued continuous functions are investigated in the case when the numberssatisfy 0 < k < 1/e and 1/e < L < 1. The present result improves almost all results of the literature concerning it. Furthermore, it is established that all solutions of the odd-order neutral delay differential equationwhere , are oscillatory ifThis result generalizes a theorem of Gopalsamy et. al (Czech. Math. J., 42 (1992),313-323) and also extends a very well-known result of Ladas (Applicable Analysis, 9(1979),93-98).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
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.
基金Supported by Natural Science Foundation of Hebei Province（102160） and Natural Science of Education office in Hebei Province （2004123）,
文摘This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations, and these results are illustrated by some examples.
基金Supported by NNSFC, RFDP and Yunnan Edu. Project
文摘Sufficient conditions for the oscillation of the neutral equation d/dt[x(t) - R(t)x(t - r)] + P(t)x(t - r) - Q(t)x(t - δ) = 0,where P,Q,R ∈ C([t0,∞), R+), and r, T, δ ∈ (0,∞), are obtained for the case where former results can not be applied.
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).
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.
文摘The problem of oscillation of neutral delay differential equations is of theoretical as well as practical interest, and the oscillation theory of such equations has been extensively developed during the past few years. However, almost all the known results deal with the equations only with positive coefficients.
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.
基金The National Natural Science Foundation of China (No.10671078)
文摘This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.
文摘Oscillation criteria are established for third-order neutral delay differential equations with deviating arguments. These criteria extend and generalize those results in the literature. Moreover, some illustrating examples are also provided to show the importance of our results.
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.
文摘In this paper,we study one type of odd-order neutral delay differential equation. Suffcient conditions for the oscillation of every solution to this type of differential equation are given.
文摘Abstract In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.
文摘In this paper, a new sufficient condition for the oscillation of all solutions of first order neutral delay differential equations is obtained. Secondly, the result can also be extended to a general neutral differential equation, and many known results in the literatures are improved.
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 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Oscillation criteria for the delay differential equationwhere p, T are non-negative real-valued continuous functions are investigated in the case when the numberssatisfy 0 < k < 1/e and 1/e < L < 1. The present result improves almost all results of the literature concerning it. Furthermore, it is established that all solutions of the odd-order neutral delay differential equationwhere , are oscillatory ifThis result generalizes a theorem of Gopalsamy et. al (Czech. Math. J., 42 (1992),313-323) and also extends a very well-known result of Ladas (Applicable Analysis, 9(1979),93-98).
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.
