Ordinary differential equations in the oscillation theory of partial half-linear differential equation

In the paper we study the damped half-linear partial differential equation div(A(x)parallel to del(u)parallel to(p-2) del u)+((b) over bar (x), parallel to del u parallel to)(p-2) del u)+c(x)vertical bar u vertical bar(p-2)u=0. Using radialization method we derive general oscillation results which allow to deduce new oscillation criteria for this equation from oscillation criteria for ordinary differential equations. Using careful radialization we improve several known oscillation criteria. (c) 2007 Elsevier Inc. All rights reserved.