Roman Koplatadze

On Oscillatory Properties of Solutions of Functional Differential Equations

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.