Oscillation criteria for neutral half-linear differential equations without commutativity in deviating arguments

We study the half-linear neutral differential equation [ r(t)Φ(z′(t)) ]′ + c(t)Φ(x(σ(t))) = 0, z(t) = x(t) + b(t)x(τ(t)), where Φ(t) = |t|p−2t. We present new oscillation criteria for this equation in case when σ(τ(t)) 6= τ(σ(t)) and ∫ ∞ r1−q(t)dt < ∞, q = p/(p− 1), p ≥ 2 is a real number. The results of this paper complement our previous results in case when the above integral is divergent and/or the deviations τ, σ commute with respect to their composition.