ASYMPTOTIC BEHAVIOR OF KNESER’S SOLUTION FOR SEMI-CANONICAL THIRD-ORDER HALF-LINEAR ADVANCED NEUTRAL DIFFERENTIAL EQUATIONS

Abstract

In this paper, we study the properties of positive solutions of the thirdorder neutral differential equations with advanced argument of the form (p(t)(q(t)(z′(t))α)′)′ + f(t)xα(τ (t)) = 0, where z(t) = x(t) + g(t)(x(σ(t))). First we obtain conditions for the existence of Kneser type solutions and then provide lower and upper estimate that yield the rate of convergence to zero of such solutions. An example is provided to illustrate the importance of the main results.