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

The third-order nonlinear functional differential equations of the form (r2(t)(r1(t)y′)′)′+p(t)y′+q(t)f(y(g(t)))=0(r2(t)(r1(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.