Forced oscillation of higher-order nonlinear differential equations

Some new criteria have been established for the oscillation of higher-order forced nonlinear differential equation of the form Lnx(t) + q(t)F(x(t)) = e(t) according to the smart choice of a class of new auxiliary functions. No restriction is imposed on the forcing term e(t) as those assumed in [A.G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. Math. Soc. 33 (1972) 377–383; A.G. Kartsatos, Recent results on oscillation of solutions of forced and perturbed nonlinear differential equations of even order, in: Stability of Dynamical Systems: Theory and Applications, Marcel Dekker, New York, 1977, pp. 17–72]. The main results of this paper are different from most known ones in the sense that they are given in the form lim inft→∞[·] < 0