Periodic solutions of resonant systems with rapidly rotating nonlinearities. (English) Zbl 1250.34034
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.
Reviewer: Jean Mawhin (Louvain-La-Neuve)
MSC:
34C25 | Periodic solutions to ordinary differential equations |
47N20 | Applications of operator theory to differential and integral equations |