The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of a...The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.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 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
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, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions fo...In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.展开更多
Abstract In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.
This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequal...This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.展开更多
By employing the generalized Riccati transformation technique,we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral del...By employing the generalized Riccati transformation technique,we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation [r(t)[y(t)+p(t)y(■(t))]~Δ]~Δ+q(t)f(y((δ(t)))=0 on a time scale■.The results improve some oscillation results for neutral delay dynamic equations and in the special case when■our results cover and improve the oscillation results for second- order neutral delay differential equations established by Li and Liu[Canad.J.Math.,48(1996), 871 886].When■,our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh[Comp.Math.Appl.,36(1998),123-132].When ■ ■our results are essentially new.Some examples illustrating our main results are given.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
Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The ...Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.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
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
In this paper, we consider a class of second-order neutral delay dynamic equations on a time scale T. By means of Riccati transformation technique, we establish some new oscillation criteria in two different condition...In this paper, we consider a class of second-order neutral delay dynamic equations on a time scale T. By means of Riccati transformation technique, we establish some new oscillation criteria in two different conditions. The obtained results enrich the well-known oscillation results for some dynamic equations.展开更多
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
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.
Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some i...Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.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
By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend some known results in the previous lit...By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend some known results in the previous literatures.展开更多
This paper is concerned with the following nonlinear delay differential equation with nonlinear neutral term[h(t)(y(t) +φ(t,y(τ(t)))']' + q(t)f(y(g(t))) = 0. An oscillation criterion for the above equation i...This paper is concerned with the following nonlinear delay differential equation with nonlinear neutral term[h(t)(y(t) +φ(t,y(τ(t)))']' + q(t)f(y(g(t))) = 0. An oscillation criterion for the above equation is obtained.展开更多
In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we es...In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation.展开更多
基金Project supported by the National Education Committee Doctoral Foundation of China (20020558092)
文摘The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.
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 the National Natural Science Foundation of China(10471086).
文摘In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.
文摘Abstract In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.
基金Supported by the NNSF of China(11071222)Supported by the NSF of Hunan Province(12JJ6006)Supported by Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)
文摘This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.
文摘By employing the generalized Riccati transformation technique,we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation [r(t)[y(t)+p(t)y(■(t))]~Δ]~Δ+q(t)f(y((δ(t)))=0 on a time scale■.The results improve some oscillation results for neutral delay dynamic equations and in the special case when■our results cover and improve the oscillation results for second- order neutral delay differential equations established by Li and Liu[Canad.J.Math.,48(1996), 871 886].When■,our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh[Comp.Math.Appl.,36(1998),123-132].When ■ ■our results are essentially new.Some examples illustrating our main results are given.
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Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.
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, 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supported by the Youth Foundation of Anqing Teachers College(KJ201107)the General Foundation of the Education Department of Anhui Province(AQKJ2014B010)
文摘In this paper, we consider a class of second-order neutral delay dynamic equations on a time scale T. By means of Riccati transformation technique, we establish some new oscillation criteria in two different conditions. The obtained results enrich the well-known oscillation results for some dynamic equations.
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).
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Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.
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By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend some known results in the previous literatures.
基金This work is supported by National Natural Sciences Foundation of ChinaNatural Sciences Foundation of Yunnan Province.
文摘This paper is concerned with the following nonlinear delay differential equation with nonlinear neutral term[h(t)(y(t) +φ(t,y(τ(t)))']' + q(t)f(y(g(t))) = 0. An oscillation criterion for the above equation is obtained.
基金the Natural Science Foundation of Hunan Province under Grant 05JJ40008.
文摘In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation.
