ON HIGHER ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS WITH PROPERTY A

Abstract. We study oscillatory properties of solutions of a functional dif-ferential equation of the form u(n)(t) + F (u)(t) = 0, where n ≥ 2 and F: C(R+;R) → Lloc(R+;R) is a continuous mapping. Sufficient conditions for this equation to have the so-called Property A are established. In the case of ordinary differential equation the obtained results lead to an integral generalization of the well-known theorem by Kondrat’ev