In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for ...In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for oscillation are presented.展开更多
In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are establishe...In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.展开更多
Sufficient conditions are obtained for the oscillation of solutions of the systems of quasilinear hyperbolic differential equation with deviating arguments under nonlinear boundary condition.
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,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 making use of the integral inequalities and some results of the functional differential equations, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations of neutral type ...By making use of the integral inequalities and some results of the functional differential equations, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations of neutral type with multi-delays were investigated and a series of sufficient conditions for oscillations of the equations were established. The results fully indicate that the oscillations are caused by delay and hence reveal the difference between these equations and those equations without delay.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
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.
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
Consider the second order nonlinear neutral delay differential equaiton[α(t)|(x(t)+p(t)x(t-τ))′| α-1 (x(t)+p(t)x(t-τ))′]′+q(t)|x(t-σ)| α-1 x(t-σ)=0. We obtain a sufficient condition for the oscillati...Consider the second order nonlinear neutral delay differential equaiton[α(t)|(x(t)+p(t)x(t-τ))′| α-1 (x(t)+p(t)x(t-τ))′]′+q(t)|x(t-σ)| α-1 x(t-σ)=0. We obtain a sufficient condition for the oscillation of all solutions of the above equation, our result extend and improve the result in .展开更多
In this paper the sufficient conditions are obtained for oscillation of neutral nonlinearhyperbolic equations with doubled variable coefficients. These results are illustrated bysome examples.
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
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
This paper, deals with the oscillatory properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results ...This paper, deals with the oscillatory properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results reveal that the varied difference between hyperbolic functional differential equations and hyperbolic differential equations.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
Consider the second order nonlinear neutral difference equationThe sufficient conditions are established for the oscillation and asymptotic behavior of the solutions of this equation.
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
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
Consider the second Order nonlinear neutral difference equation for n≥n0 The sufficient conditions are obtained for the oscillatory and asymptotic behavior of the solutions of this equation.
A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the crite...A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the criteria existing in literature. Our conditions are necessary and suffcient when all the coeffcients of the equations are constants.展开更多
文摘In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for oscillation are presented.
文摘In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.
基金This work is supported in part by NNSF of China(10571126)and in part by Program for New Century Excellent Talents in University.
文摘Sufficient conditions are obtained for the oscillation of solutions of the systems of quasilinear hyperbolic differential equation with deviating arguments under nonlinear boundary condition.
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 making use of the integral inequalities and some results of the functional differential equations, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations of neutral type with multi-delays were investigated and a series of sufficient conditions for oscillations of the equations were established. The results fully indicate that the oscillations are caused by delay and hence reveal the difference between these equations and those equations without delay.
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.
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Consider the second order nonlinear neutral delay differential equaiton[α(t)|(x(t)+p(t)x(t-τ))′| α-1 (x(t)+p(t)x(t-τ))′]′+q(t)|x(t-σ)| α-1 x(t-σ)=0. We obtain a sufficient condition for the oscillation of all solutions of the above equation, our result extend and improve the result in .
文摘In this paper the sufficient conditions are obtained for oscillation of neutral nonlinearhyperbolic equations with doubled variable coefficients. These results are illustrated bysome examples.
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This work is supported by the Natural Science Foundation of Hubei Province.
文摘This paper, deals with the oscillatory properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results reveal that the varied difference between hyperbolic functional differential equations and hyperbolic differential equations.
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.
文摘Consider the second order nonlinear neutral difference equationThe sufficient conditions are established for the oscillation and asymptotic behavior of the solutions of this equation.
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.
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Consider the second Order nonlinear neutral difference equation for n≥n0 The sufficient conditions are obtained for the oscillatory and asymptotic behavior of the solutions of this equation.
文摘A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the criteria existing in literature. Our conditions are necessary and suffcient when all the coeffcients of the equations are constants.
