New Kamenev-type oscillation criteria for half-linear partial differential equations

作者：Yang, Ge-feng; Xu, Zhi-ting^*

来源：Acta Mathematicae Applicatae Sinica-English Series, 2012, 28(3): 535-548.

DOI：10.1007/s10255-012-0168-0

• oscillation
• half-linear
• partial differential equations
• Kamenev-type
• Damped equation

We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping @@@ div(A(x)parallel to del u parallel to(p-2)del u) + < b(x), parallel to del u parallel to(p-2)del u > + c(x)vertical bar u vertical bar(p-2)u = 0 @@@ under quite general conditions. These results are extensions of the recent results developed by Sun [Y.G. 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.

• 出版日期2012-7
• 单位广东外语外贸大学; 华南师范大学