R. Koplatadze

On Higher Order Functional Differential Equations with Property A

Abstract:
We study oscillatory properties of solutions of a functional differential equation of the form
$$ u^{(n)}(t)+F(u)(t)=0, $$
where $n\geq 2$ and $F:C(R_+;R)\to L_{loc}(R_+;R)$ is a continuous mapping. Sufficient conditions for this equation to have the so-called Property A are established. In the case of ordinary differential equation the obtained results lead to an integral generalization of the well-known theorem by Kondrat'ev.

Keywords:
Functional differential equations, oscillatory solution, Property A, proper solution.

MSC 2000: 34C10, 34K11.