Periodic solutions for differential systems in R3 and R4

We provide sufficient conditions for the existence of periodic solutions for the differential systems x' = y, y' = z, z' = -y - epsilon F(t, x, y, z), and x' = y, y' = -x - epsilon G(t, x, y, z, u), z' = u, u' = -z - epsilon H(t, x, y, z, u) where F, G and H are 2 pi-periodic functions in the variable t and epsilon is a small parameter. These differential systems appear frequently in many problems coming from the sciences and the engineering.

Automated summary

Sufficient conditions are provided for the existence of periodic solutions in differential systems, which are often encountered in scientific and engineering problems.