In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain fu...In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.展开更多
By an associate linear equation, we obtain a linearized oscillation result of certain odd-order nonlinear neutral delay differential equation. The result answers partially an open problem proposed by Gyori and Ladas.
Consider the nonlinear neutral delay differential equationwhere P, Q ∈ C([t0,∞),R), τ > 0, δ > 0. We obtain a linearized oscillation result by an associate linear equation in the case when liminfP(t) = p0 ∈...Consider the nonlinear neutral delay differential equationwhere P, Q ∈ C([t0,∞),R), τ > 0, δ > 0. We obtain a linearized oscillation result by an associate linear equation in the case when liminfP(t) = p0 ∈[-1,0).展开更多
We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping div(A(x)|| u||^p-2 u)+〈b(x),|| u||^p-2 u〉+c(x)|u|^p-2u=0(E)under quite general ...We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping div(A(x)|| u||^p-2 u)+〈b(x),|| u||^p-2 u〉+c(x)|u|^p-2u=0(E)under quite general conditions. These results are extensions of the recent results developed by Sun [Y.C. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations.展开更多
Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some r...Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some results in parts of the relative references.展开更多
基金partially supported by the construct program of the key disciplin in Hunan Province(No.070105)
文摘In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.
基金This work is supported by the NNSF of China (No. 10071018).
文摘By an associate linear equation, we obtain a linearized oscillation result of certain odd-order nonlinear neutral delay differential equation. The result answers partially an open problem proposed by Gyori and Ladas.
基金This work is supported by the NNSF of China(No.10071018).
文摘Consider the nonlinear neutral delay differential equationwhere P, Q ∈ C([t0,∞),R), τ > 0, δ > 0. We obtain a linearized oscillation result by an associate linear equation in the case when liminfP(t) = p0 ∈[-1,0).
基金Supported by the National Natural Science Foundation of Guangdong Province under Grant (No.8451063101000730)
文摘We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping div(A(x)|| u||^p-2 u)+〈b(x),|| u||^p-2 u〉+c(x)|u|^p-2u=0(E)under quite general conditions. These results are extensions of the recent results developed by Sun [Y.C. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations.
基金Supported by Science Foundation of Educational Department of Guangdong Province(Z03052).
文摘A kind of second-order half-linear differential equations with impulses is studied in this paper. Our results improve and generalize some known ones.
基金A project supported by Scientific Research Fund of Hunan Provincial Education Department.
文摘Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some results in parts of the relative references.