Periodic solutions of first-order autonomous quasi-linear systems

In this paper, using topological degree and linear algebra techniques, we prove that a certain class of quasi-linear systems of differential equations of the formx˙=Ax+μf(x,μ)has at least one periodic solution, where μμ is a small parameter and AA is a constant n×nn×n matrix. If μμ is bounded away from zero and the components of ff are polynomials in x1,…,xn,μx1,…,xn,μ, then there exists at least one periodic solution under certain conditions. Finally, we consider several examples.