We study the existence of large-amplitude periodic or almost periodic solutions of second order differential equations with asymmetric nonlinearities, when the system is close to "nonlinear resonance".
Fabry, C., & Fonda, A. (2000). Bifurcations from infinity in asymmetric nonlinear oscillators. No D E A - Nonlinear Differential Equations and Applications, 7(1), 23-42. https://doi.org/10.1007/PL00001421 (Original work published 2000)