Dynamics of Third-Order Nonlinear Neutral Equations

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear neutral equation with continuously distributed delays of the form (r(t) ([x(t) + integral(b)(a) p(t, mu) x[tau(t, mu)] d mu]")(alpha))' + integral(d)(c) q(t, xi) f(alpha) (x[g(t,xi)]d xi = 0 Applying suitable generalized Riccati transformation and integral averaging technique, we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of this equation. Obtained results essentially improve and complement earlier ones.