Quasi-periodic solutions for perturbed autonomous delay differential equations (Q765950)

The authors investigate the existence of quasi-periodic solutions of the autonomous delay differential equation in \({\mathbb{R}}^n\) \[ x^{\prime}(t)=A(\xi)x(t)+B(\xi)x(t-\tau)+\varepsilon f(x(t), x(t-\tau), \xi, \varepsilon) \] under the condition that the unperturbed equation (i.e., the equation obtained from the above one for \(\varepsilon =0\)) has a quasi-periodic solution, where \(A, \, B\) are \(n\times n\) matrices, \(\tau >0\), \(\xi \) is an \(n_0\) dimensional parameter, and \(\varepsilon >0\) is a small parameter. More precisely, the paper establishes persistence of quasi-periodic solutions under small perturbations.