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 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
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.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.
Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and ...Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.展开更多
The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging techniq...The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging technique. Some well known results in the literature are extended. Moreover, two examples are given to illustrate the theoretical analysis.展开更多
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
This paper discusses the oscillation of second-order nonlinear differential equations with impulses. Sufficient conditions for all solutions of the equation to be oscillated are obtained.
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
At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to ...At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.展开更多
In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example tha...In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example that dwells upon the sharp conditions of our result is also included.展开更多
Some oscillation theorems are given for the nonlinear second order elliptic equation N∑i,j=1 Di[aij（x）ψ（y）｜｜△↓y｜｜^p-2 Djy]＋c（x）f（y）=0The results are extensions of modified Riccati techniques and inclu...Some oscillation theorems are given for the nonlinear second order elliptic equation N∑i,j=1 Di[aij（x）ψ（y）｜｜△↓y｜｜^p-2 Djy]＋c（x）f（y）=0The results are extensions of modified Riccati techniques and include recent results of Usami.展开更多
Sufficient conditions to guarantee all solutions to be oscillatory of a second order nonlinear impulsive difference equation are obtained by using Riccati transformation.
The present paper is devoted to the investigation of the oscillation of second order nonlinear delay differential equation （DDE） with impulses, sufficient conditions of oscillation for the solutions of DDE with impu...The present paper is devoted to the investigation of the oscillation of second order nonlinear delay differential equation （DDE） with impulses, sufficient conditions of oscillation for the solutions of DDE with impulses are obtained by using differential inequality. Some known results are improved and generalized.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
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 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By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
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Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.
文摘The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging technique. Some well known results in the literature are extended. Moreover, two examples are given to illustrate the theoretical analysis.
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
基金the Foundation of Binzhou University (BZXYQMG200622)the Foundation of Educational Department of Shandong Province (J07WH01)
文摘This paper discusses the oscillation of second-order nonlinear differential equations with impulses. Sufficient conditions for all solutions of the equation to be oscillated are obtained.
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.
基金supported by the National Natural Science Foundation of China (No.1097123131071560)+1 种基金the NSF of Guangdong Province (No.101510225010000048151027501000053)
文摘At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.
基金Supported by the NNSF of China (11161049)the SF of the Zhangjiakou Bureau of Science and Technology (1112027B-1)
文摘In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example that dwells upon the sharp conditions of our result is also included.
文摘Some oscillation theorems are given for the nonlinear second order elliptic equation N∑i,j=1 Di[aij（x）ψ（y）｜｜△↓y｜｜^p-2 Djy]＋c（x）f（y）=0The results are extensions of modified Riccati techniques and include recent results of Usami.
基金Partially supported by Guangdong Natural Science Foundation (980018).
文摘Sufficient conditions to guarantee all solutions to be oscillatory of a second order nonlinear impulsive difference equation are obtained by using Riccati transformation.
文摘The present paper is devoted to the investigation of the oscillation of second order nonlinear delay differential equation （DDE） with impulses, sufficient conditions of oscillation for the solutions of DDE with impulses are obtained by using differential inequality. Some known results are improved and generalized.
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.
