Oscillation criteria for forced second order quasi-linear PDE with damping

Abstract

The oscillation criteria developed by Nasr and Wong are extended to the forced second order quasi-linear PDE with damping div(4(x)|Λu|p- 2Λu) + (b(x), |Λu|P-2Λu) + c(u)|u|^q-2u = e(x). When N = 1, for some forced second order nonlinear ordinary differential equations, our results include the recent results due to Li and and Cheng, Xing and Zheng, Yang, Zheng and Meng. When N > 2, our results are more general, and improve the oscillation criteria of Zhuang for a forced second order undamped elliptic differential equation.