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 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, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation ar...In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.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
In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions ...In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.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, we will study generic oscillation and generic nonoscillation of first order impulsive delay differential equations. A necessary and sufficient condition and some sufficient conditions are obtained for b...In this paper, we will study generic oscillation and generic nonoscillation of first order impulsive delay differential equations. A necessary and sufficient condition and some sufficient conditions are obtained for both phenomena based on the root of characteristic equation.展开更多
Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained ...Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained for all solutions to be oscillatory when the equation is of oscillating coefficients.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
In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses. Some new sufficient conditions which guarantee that every solution is oscillatory or converges ...In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses. Some new sufficient conditions which guarantee that every solution is oscillatory or converges to zero are obtained. Three examples are also given to illustrate our main results.展开更多
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 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This work is supported by National Natural Science Foundation of China (40373003 and 40372121).
文摘In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.
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.
基金This research is supported by National Natural Science Foundation of China (No.10361003).
文摘In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.
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.
文摘In this paper, we will study generic oscillation and generic nonoscillation of first order impulsive delay differential equations. A necessary and sufficient condition and some sufficient conditions are obtained for both phenomena based on the root of characteristic equation.
文摘Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained for all solutions to be oscillatory when the equation is of oscillating coefficients.
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.
文摘In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses. Some new sufficient conditions which guarantee that every solution is oscillatory or converges to zero are obtained. Three examples are also given to illustrate our main results.
文摘By a Riccati transformation, we establish some new oscillation criteria which im-prove and generalize some known results in the previous literatures.