Limit and Integral Properties of Principal Solutions for Half-linear Differential equations

Some asymptotic properties of principal solutions of the half-linear differential equation (*) (a(t)Φ(x′))′+ b(t)Φ(x) =0, Φ(u) = |u|p-2u, p > 1, is the p-Laplacian operator, are considered. It is shown that principal solutions of (*) are, roughly speaking, the smallest solutions in a neighborhood of infinity, like in the linear case. Some integral characterizations of principal solutions of (1), which completes previous results, are presented as well.