Accession Number : AD0627134

Title :   PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS AND SOLUTIONS OF FUNCTIONAL EQUATIONS BY TOPOLOGICAL METHODS.

Descriptive Note : Final rept., 1 Jan 62-31 Dec 65,

Corporate Author : POLYTECHNIC INST OF BROOKLYN N Y

Personal Author(s) : Scanlon,Jane Cronin

Report Date : 31 DEC 1965

Pagination or Media Count : 2

Abstract : The problem studied is that of the existence of periodic solutions of a system (in vector notation) (E) x = f(x,t) where f has period T in variable t, i.e., a nonautonomous system with 'large' nonlinearities. Previously known results on this problem are largely restricted to the 2dimensional case except for a few results for the 3dimensional case. Results and conclusions reached: A new technique for establishing the existence of periodic solutions of (E) was developed for the 2-dimensional case. The technique consists in studying the behavior of solutions of (E) near the point at infinity by studying the stability of the origin as a critical point of the system obtained by performing an inversion transformation on (E). Practical sufficient conditions for stability and asymptotic stability (i.e., conditions which can be verified by straight-forward computation) were derived. The technique developed for the 2-dimensional case was extended to the n-dimensional case and new existence theorems for periodic solutions were derived. (Document quoted in its entirety)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, TOPOLOGY), (*TOPOLOGY, NONLINEAR DIFFERENTIAL EQUATIONS), (*EQUATIONS, TOPOLOGY), STABILITY, TRANSFORMATIONS(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE