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

We study the half-linear neutral differential equation [r(t)Phi(z'(t))]' + c(t)Phi(x(sigma(t))) = 0, z(t) = x(t) + b(t)x(tau(t)), where Phi(t) = vertical bar t vertical bar(p) (2)t. We present new oscillation criteria for this equation in case when sigma(tau(t)) not equal tau(sigma(t)) and integral(infinity)r(1q)(t) dt < infinity, q = p/(p-1), p >= 2 is a real number. The results of this paper complement our previous results in case when the above intergal is divergent and/or the deviations tau, sigma commute with respect to their composition.