This paper considers existence of periodic solutions for vector Liénard differential equations
In our main result we write
where Q(t, x) is a symmetric matrix and h(t, x) is sublinear. The key assumption relates the asymptotic behaviour as x →+ ∞ of the eigenvalues of Q(t, x) to the spectrum of the linear operator −d2/dt2 Several choices for Q(t, x) are considered which lead to known theorems and extend others. In the case of the Duffing equation
the assumptions are weakened.
Our approach is based on Leray-Schauder's degree theory and a priori estimates.