Computer-assisted proof of a periodic solution in a nonlinear feedback DDE (Q1039214)

For the delay equation \[ x'(t) = -K \sin(x(t-1)), \] existence of periodic solutions is proved with computer assistance, employing a Fourier series ansatz. Using a homotopy method and the Brouwer degree, it is shown that the equation for the Fourier coefficients has a solution in a space of sequences decaying like \(1/n^2\). Main methods are the convolution of convergent Fourier series and a suitable splitting in `lower' (\(< 225\)) and `higher' Fourier modes. The author remarks that the observed period is apparently 4, but that he could not prove this -- obviously the observed solutions are the well-known special symmetric solutions (Kaplan-Yorke solutions).