Accession Number : AD0725051

Title :   Oscillations in Neutral Functional Differential Equations,

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Hale,Jack K.

Report Date : JUN 1971

Pagination or Media Count : 23

Abstract : A neutral functional differential equation as defined below includes the scalar differential-difference equation (1) d/dt(x(t)+ax(t-1)+ epsilon G(t,x(t-1))) = bx(t)+cx(t-1)+ epsilon F(t,x(t),x(t-1)) where epsilon is a parameter, a,b,c are constants and G(t,x), F(t,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 x(t) + ax(t-1) + G(x(t-1)) (not x(t)) 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 :   (*DIFFERENTIAL EQUATIONS, *NUMERICAL INTEGRATION), BANACH SPACE, DIFFERENCE EQUATIONS, INTEGRAL EQUATIONS, MATRICES(MATHEMATICS), PERTURBATION THEORY, TRANSCENDENTAL FUNCTIONS, PERIODIC VARIATIONS, TOPOLOGY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE