Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term

Abstract

In this paper, the oscillation property and the asymptotic behavior of solutions of neutral second-order differential Equations of the Emden-Fowler type were studied under the influence of the coefficients of forces. It has been shown through this research that the coefficients of forces in addition to the Emden-Fowler type have a major role on the oscillation of solutions of neutral Equations. As well as its effect on the convergence and divergence of nonoscillatory solutions. For this purpose, some conditions are obtained to ensure that all solutions of the neutral Equations Emden-Fowler type oscillating or nonoscillating go to ∞, as t → ∞. Some of these conditions are the development of conditions similar to them in some of the well-known results included in the references, for example, condition (8) in this research with condition (4) in (9). The obtained results included some illustrative examples showing that the resulting conditions are easy to apply and guarantee oscillation.

Keywords

• Oscillation, Asymptotic behavior, Emden-Fowler, Forcing Term.