**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.