
Accession Number : AD0627134
Title : PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS AND SOLUTIONS OF FUNCTIONAL EQUATIONS BY TOPOLOGICAL METHODS.
Descriptive Note : Final rept., 1 Jan 6231 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 2dimensional 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 straightforward computation) were derived. The technique developed for the 2dimensional case was extended to the ndimensional 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