Large-Amplitude Periodic Oscillations in Simple and Complex Mechanical Systems: Outgrowths from Nonlinear Analysis

In this paper, we survey developments in nonlinear partial differential equations and applications since the original paper of Ambrosetti and Prodi on nonlinearities that cross eigenvalues. We show how this work has important developments in nonlinear analysis, and survey the implications for periodically forced mechanical systems, from simple one-particle vibrating systems to suspension bridges and ships. Lecture held in the Seminario Matematico e Fisico on March 9, 2005 Received: December 2005