Generic results for the existence of nondegenerate periodic solutions of some differential systems with periodic nonlinearities (original) (raw)

This paper addresses the existence of nondegenerate periodic solutions for certain differential systems featuring periodic nonlinearities. Utilizing Sard's theorem in an infinite-dimensional context, the work establishes conditions under which regular values in certain spaces are dense and open. Key examples include the forced pendulum equation and Hamiltonian systems, demonstrating that these periodic problems yield multiple distinct solutions under specific constraints. The findings enhance the understanding of periodic solutions in differential equations, providing a framework for further exploration of related mathematical phenomena.