
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 differentialdifference equation (1) d/dt(x(t)+ax(t1)+ epsilon G(t,x(t1))) = bx(t)+cx(t1)+ epsilon F(t,x(t),x(t1)) 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(t1) + G(x(t1)) (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