Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities (Q6153093)

The authors prove the existence of a miriad of periodic solutions for a system of second order differential equations with a parameter, generalizing a similar result for scalar equations in [\textit{A. Boscaggin} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 12, 4457--4470 (2012; Zbl 1278.34038)]. The nonlinearities have a singularity of repulsive type at the origin and linear growth at infinity. The proof is based on a higher dimensional Poincaré-Birkhoff theorem by Fonda and Ureña.