# Accession Number:

## AD0725051

# Title:

## Oscillations in Neutral Functional Differential Equations,

# Descriptive Note:

# Corporate Author:

## BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

# Personal Author(s):

# Report Date:

## 1971-06-01

# Pagination or Media Count:

## 23.0

# Abstract:

A neutral functional differential equation as defined below includes the scalar differential-difference equation 1 ddtxtaxt-1 epsilon Gt,xt-1 bxtcxt-1 epsilon Ft,xt,xt-1 where epsilon is a parameter, a,b,c are constants and Gt,x, Ft,x,y are continuous functions of t,x,y. For any continuous function phi defined on -1,0, a solution of 1 is a continuous function x defined on some interval -1, alpha, alpha 0, which coincides with phi on -1,0 and is such that the expression xt axt-1 Gxt-1 not xt is continuously differentiable and satisfies 1 on 0, alpha. The purpose of this paper is to prove for epsilon small the existence of bounded and periodic solutions of 1. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics