Oscillations of forced functional differential equations generated by advanced arguments

Abstract

This paper is concerned with the oscillatory and asymptotic behavior of the solutions of the forced functional differential equations with advanced arguments of the form d/dt 1/an-1(t) d/dt 1/an-2 (t) ... d/dt 1/a1(t) d/dt x(t) + δf(t, x[g1 (t)], ..., x[gm(t)]) = Q(t), (E, δ) where δ = ±1. Conditions which ensure that every solution of the equation (E, 1) is oscillatory or tending to zero as t → ∞ are given. A classification of all solutions of the equation (E, -1) with respect to their behavior as t → ∞ and to their oscillatory character is also obtained. Finally, the sufficient conditions so that all solutions of the equation (E, δ) are oscillatory or tending to zero as t → ∞ are presented. The obtained results extend and unify recent ones by Werbowski. © Birkhäuser Verlag, 2002.