On the existence of periodic solutions for periodic quasilinear ordinary differential systems (Q1096765)

The authors deal with the problem of the existence of T-periodic solutions for the T-periodic quasilinear ordinary differential system (1) \(x' = A(t,x)x + F(t,x)\) where \(A(t,x)\) is a real n x n matrix continuous in \((t,x)\) and T-periodic in \(t\). Consider the associated linear system (2) \(x' = B(t)x\) where \(B(t)\) is a real \(n\times n\) matrix continuous and T-periodic in T. The main result shows how \(A(t,x)\) in (1) is close to \(B(t)\) in (2) and obtains certain conditions of \(F(t,x)\) which are weaker than the known results.