Resumen de Periodic solutions for differential systems in R 3 and R 4

Amina Feddaoui, Jaume Llibre , Chemseddine Berhail, Amar Makhlouf

• We provide sufficient conditions for the existence of periodic solutions for the differential systems x 0 = y, y 0 = z, z 0 = −y−εF(t, x, y,z), and x 0 = y, y 0 = −x−εG(t, x, y,z,u), z 0 = u, u 0 = −z−εH(t, x, y,z,u), where F, G and H are 2π–periodic functions in the variable t and ε is a small parameter. These differential systems appear frequently in many problems coming from the sciences and the engineering.