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

Abstract

We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping $$div(A(x)\left\| {\nabla u} \right\|^{p - 2} \nabla u) + \left\langle {b(x),\left\| {\nabla u} \right\|^{p - 2} \nabla u} \right\rangle + c(x)\left| u \right|^{p - 2} u = 0$$ (E) 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.