
Accession Number : AD0681064
Title : ASYMPTOTIC BEHAVIOUR OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS,
Corporate Author : CALIFORNIA UNIV LOS ANGELES
Personal Author(s) : Hale,Jack K. ; Cruz,Marianito A.
Report Date : 1968
Pagination or Media Count : 43
Abstract : A functional differential equation of neutral type is an equation for a function x in which the derivative x dot of x at time t depends not only upon the past and present values of x, but also upon the past and present values of x dot. A general class of linear functional differential equations of neutral type is defined in the space of continuous functions. For this class, a variation of constants formula is derived which gives the solution of a nonhomogeneous linear equation with zero initial data as an integral of the forcing function. It is then shown that the kernel in this integral representation can be used to obtain the general solution of the homogeneous equation. The stability properties of the solutions of the homogeneous equation are characterized in terms of the kernel in the variation of constants formula. Section 3 is devoted to the stability of solutions of equations which are linear or nonlinear perturbations of a given linear system. (Author)
Descriptors : (*FUNCTIONAL ANALYSIS, DIFFERENTIAL EQUATIONS), (*DIFFERENTIAL EQUATIONS, STABILITY), DIFFERENCE EQUATIONS, PERTURBATION THEORY, PERIODIC VARIATIONS, VECTOR SPACES, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE