By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.
It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential. A formally exact solution of the timedependent Gross-Pitaevskii equation is constructed, which describes the matter shock waves with chaotic or periodic amplitudes and phases.
