By employing a generalized Riccati technique and an integral averaging tech-nique, new interval oscillation criteria are established for the forced second-order half-lineardifferential equation [r(t)|x′ (t)|α-1x′ (...By employing a generalized Riccati technique and an integral averaging tech-nique, new interval oscillation criteria are established for the forced second-order half-lineardifferential equation [r(t)|x′ (t)|α-1x′ (t)]′ + q(t)|x(t)|α-1x(t) = e(t).展开更多
This paper discusses a class of forced second-order half-linear differential equations. By using the generalized Riccati technique and the averaging technique, some new interval oscillation criteria are obtained.
By employing the inequality of [8] and a positive continuous function g（t）, t[t0, ＋∞）, oscillation criteria for the second-order half-linear impulsive differential equ-ations with damping are established. Our res...By employing the inequality of [8] and a positive continuous function g（t）, t[t0, ＋∞）, oscillation criteria for the second-order half-linear impulsive differential equ-ations with damping are established. Our results generalize and improve some known ones.展开更多
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
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
文摘By employing a generalized Riccati technique and an integral averaging tech-nique, new interval oscillation criteria are established for the forced second-order half-lineardifferential equation [r(t)|x′ (t)|α-1x′ (t)]′ + q(t)|x(t)|α-1x(t) = e(t).
文摘This paper discusses a class of forced second-order half-linear differential equations. By using the generalized Riccati technique and the averaging technique, some new interval oscillation criteria are obtained.
基金Foundation item： Supported by the Natural Science Foundation of Guangdong Province（011471）
文摘By employing the inequality of [8] and a positive continuous function g（t）, t[t0, ＋∞）, oscillation criteria for the second-order half-linear impulsive differential equ-ations with damping are established. Our results generalize and improve some known ones.
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.
