OSCILLATION OF NEUTRAL SECOND ORDER HALF-LINEAR DIFFERENTIAL EQUATIONS WITHOUT COMMUTATIVITY IN DEVIATING ARGUMENTS

In this paper we derive oscillation criteria for the second order 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, p >= 2, is a power type nonlinearity. We improve recent results published in the literature by obtaining better oscillation constants and removing the usual condition sigma(tau(t)) = tau(sigma(t)). Two methods (comparison method and Riccati equation method) are used. (C) 2017 Mathematical Institute Slovak Academy of Sciences