Some New Oscillation Results for Higher-Order Nonlinear Differential Equations with a Nonlinear Neutral Term

Abstract

The authors study the oscillatory behaviors of solutions of higher-order nonlinear differential equations with a nonlinear neutral term. The right hand side of their equation contains both an advanced and a delay term, and either (or both) of them can be sublinear or superlinear. The influence of these terms on the oscillatory and asymptotic behaviors of solutions is investigated by using a comparison to first-order advanced and delay differential equations. New oscillation criteria are presented that improve and extend many known oscillation criteria in the literature. An example is provided to illustrate the results.

Keywords

• oscillation
• asymptotic behavior
• higher-order
• nonlinear neutral term