Investigation of oscillatory conditions of weakly nonlinear systems with n degrees of freedom and with delay (Q800557)

The authors investigate quasiperiodic solutions of the following system of differential-difference equations \[ x''(t)+\lambda^ 2x=\epsilon f(x(t),x(t-\Delta),x'(t),x'(t-\Delta)), \] where \(x(t)\in {\mathbb{R}}^ n\), \(\lambda^ 2=diag(\lambda^ 2_ 1,...,\lambda^ 2_ n)\), \(\epsilon\) is a small positive parameter, \(f:{\mathbb{R}}^{4n}\to {\mathbb{R}}^ n\) is a polynomial. In particular, the conditions for the existence of an invariant torus are given.