Some recent results concerning properties of solutions of the half-linear second order differential equation (∗) (r(t)Φ(x' ))' + c(t)Φ(x)=0, Φ(x) := |x| p−2x, p > 1, are presented. A particular attention is paid to the oscillation theory of (∗). Related problems are also discussed.
The Picone-type identity for the half-linear second order partial differential equation n∑ i=1 ∂ ⁄ ∂xi Φ (∂u ⁄ ∂xi) + c(x)Φ(u) = 0, Φ(u) := |u| p−2 u, p > 1, is established and some applications of this identity are suggested.