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
In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
Consider the n-th order neutral differential equation where n > 1 is an odd integer, p(t) ∈ C([t0, ∞ ), R), Q(t), R(t)∈ C([t0, ∞), R+), τ > 0, σ, r ∈ R+. In this paper we will survey some recent results o...Consider the n-th order neutral differential equation where n > 1 is an odd integer, p(t) ∈ C([t0, ∞ ), R), Q(t), R(t)∈ C([t0, ∞), R+), τ > 0, σ, r ∈ R+. In this paper we will survey some recent results on the oscillation of Eq.() without the usual requirement that We also give some interesting open problems on this topic.展开更多
In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contractio...In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contraction mapping principle and some necessary techniques. Moreover, some sufficient conditions for oscillation of the equations are given. Some results available in documents are extended in this paper. Illustrative examples are given.展开更多
In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.
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
The solvability for a kind of singularly perturbed problem of nonlinear neutral differential difference system is considered. Using the boundary layer corrective method, the formal asymptotic solution is constructed. ...The solvability for a kind of singularly perturbed problem of nonlinear neutral differential difference system is considered. Using the boundary layer corrective method, the formal asymptotic solution is constructed. And applying the theory of fixed point, the uniform validity of the asymptotic expansions for solution is proved. Finally, an example is given to validate the results of the problems.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
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
In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
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
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
In this paper, new oscillation criteria are obtained for all solution of the firstorder neutral difference equation △(x(n) - P(n)x(n-m)) + Q(n)x(n-k) =0, n ≥n0 where m > 0, k≥ 0 are integers. p(n), Q(n)∈ C({n0...In this paper, new oscillation criteria are obtained for all solution of the firstorder neutral difference equation △(x(n) - P(n)x(n-m)) + Q(n)x(n-k) =0, n ≥n0 where m > 0, k≥ 0 are integers. p(n), Q(n)∈ C({n0, n0 + 1,...}, R+). Our results do not need the usual hypothesis ∑Q(s) = ∞. Some example are given s=N to demonstrate the advantage of our results than those in the literature.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.
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
Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some...Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.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
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
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In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
文摘Consider the n-th order neutral differential equation where n > 1 is an odd integer, p(t) ∈ C([t0, ∞ ), R), Q(t), R(t)∈ C([t0, ∞), R+), τ > 0, σ, r ∈ R+. In this paper we will survey some recent results on the oscillation of Eq.() without the usual requirement that We also give some interesting open problems on this topic.
基金Supported by the Scientific Research Fund of Education Department of Hunan Province(07C680)
文摘In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contraction mapping principle and some necessary techniques. Moreover, some sufficient conditions for oscillation of the equations are given. Some results available in documents are extended in this paper. Illustrative examples are given.
基金Supported by the Science Foundation of Fushun Petroleum Institute
文摘In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.
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 Introducing Talents Program of SIT (YJ2013-33)
文摘The solvability for a kind of singularly perturbed problem of nonlinear neutral differential difference system is considered. Using the boundary layer corrective method, the formal asymptotic solution is constructed. And applying the theory of fixed point, the uniform validity of the asymptotic expansions for solution is proved. Finally, an example is given to validate the results of the problems.
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In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
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.
文摘In this paper, new oscillation criteria are obtained for all solution of the firstorder neutral difference equation △(x(n) - P(n)x(n-m)) + Q(n)x(n-k) =0, n ≥n0 where m > 0, k≥ 0 are integers. p(n), Q(n)∈ C({n0, n0 + 1,...}, R+). Our results do not need the usual hypothesis ∑Q(s) = ∞. Some example are given s=N to demonstrate the advantage of our results than those in the literature.
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Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.
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.
