PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS AND SOLUTIONS OF FUNCTIONAL EQUATIONS BY TOPOLOGICAL METHODS.
Final rept., 1 Jan 62-31 Dec 65,
POLYTECHNIC INST OF BROOKLYN N Y
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The problem studied is that of the existence of periodic solutions of a system in vector notation E x fx,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
- Theoretical Mathematics