On the qualitative behaviors of solutions of third-order nonlinear functional differential equations

Abstract

The third-order nonlinear functional differential equations of the form ( r 2 ( t ) ( r 1 ( t ) y ′ ) ′ ) ′ + p ( t ) y ′ + q ( t ) f ( y ( g ( t ) ) ) = 0 are considered. We present some new oscillatory and asymptotic behavior of solutions of this equation by modifying a method given for second-order differential equations. Our results are applicable to nonlinear functional differential equations of the above form. Several examples are also given to illustrate the importance of our results.