Periodic solutions of resonant systems with rapidly rotating nonlinearities (Q717866)

The authors study T-periodic solutions of the differential system \[ x'' + cx' + g(x) = p(t), \] where \(c \in \mathbb R\), \(g \in C(\mathbb R^N,\mathbb R^N)\) is sublinear at infinity, \(p\) is continuous, T-periodic and has mean value zero. They show the existence of a T-periodic solution under some technical conditions upon \(g\) and the non-vanishing of the Brouwer degree \(\text{deg}(g,D,0)\) with respect to some bounded domain \(D\). In the scalar case, the assumptions are related to rapidly oscillating nonlinearities. The result is compared with earlier ones of Ruiz-Ward and Ortega-Sanchez.