**Roman Koplatadze**

## On Oscillatory Properties of Solutions of Functional Differential Equations

**abstract:**

A functional differential equation
\begin{equation}
u^{(n)}(t)+F(u)(t)=0,\tag {$1$}
\end{equation}
is considered with continuous $F:C(R_+;R)\to L_{loc}(R_+;R)$.
Oscillatory properties of proper solutions of (1) are studied. In particular
sufficient conditions are given for equation (1) to have the property
{\bf A}
or {\bf B} ($\wa$ or $\wb$) which are optimal in a certain sense. Sufficient
conditions for every solution of (1) to be oscillatory are obtained as well as
existence conditions for an oscillatory solution.
Chapter 6 is dedicated to boundary value problem (16.1)-(16.2). Sufficient
conditions are established for the existence of a unique solution, a unique
oscillatory solution and a unique bounded oscillatory solution of this problem.

**Mathematics Subject Classification:**
34K15

**Key words and phrases:**
Functional differential equation, proper solution, equations with properties
A, B, a, b, Kneser-type solution, oscillatory solution,
bounded solution, boundary value problem.