Infinitely many small bouncing solutions of Hill’s type impact oscillators nearby the origin - Wang, Chao; Wang, Zhiguo; Liu, Qihuai (Topological Methods in Nonlinear Analysis, 2025)
In this paper, we consider a class of Hill’s type impact oscillators with super-linear restoring force nearby the origin. Infinitely many small and subharmonic bouncing solutions are obtained as well as symmetric subharmonic bouncing solutions of symmetric equations. The results are mainly obtained by using phase plane analysis, a generalized Poincaré-Birkhoff twist theorem and limiting arguments.