We prove the existence of periodic solutions of a second order nonlinear ordinary differential equation whose nonlinearity is at resonance with two successive eigenvalues of the associated linear operator and satisfies some Landesman-Lazer type conditions at both of them.
Fabry, C., & Fonda, A. (1990). Periodic-solutions of Nonlinear Differential-equations With Double-resonance. Annali di Matematica Pura ed Applicata, 157, 99-116. https://doi.org/10.1007/BF01765314 (Original work published 1990)