New Kamenev-type Oscillation Criteria for Half-linear Partial Differential Equations  

作　　者：Ge-feng YANG Zhi-ting XU 

机构地区：[1]Cisco School of Informatics,Guangdong University of Foreign Studies,Guangzhou,510006,China [2]School of Mathematical Sciences,South China Normal University,Guangzhou,510631,China

出　　处：《Acta Mathematicae Applicatae Sinica》2012年第3期535-548,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of Guangdong Province under Grant (No.8451063101000730)

摘　　要：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.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.

关 键 词：OSCILLATION HALF-LINEAR partial differential equations Kamenev-type Damped equation 

分 类 号：O175.2[理学—数学] O175.7[理学—基础数学]