Nontrivial periodic solutions of second order singular damped dynamical systems (Q491330)

The authors consider a second order system of the type \[ x''+h(t)x'+a(t)x=f(t,x)+e(t), \] where all functions are continuous and \(T\)-periodic in \(t\), and the nonlinearity \(f\) has a repulsive singularity at \(x=0\). Assuming that the linear equation \(x''+h(t)x'+a(t)x=0\) with \(T\)-periodic conditions has a positive Green function, they provide some sufficient conditions for the existence of a \(T\)-periodic solution, satisfying \(x(t)\neq0\) for every \(t\). The proofs are based on the Leray--Schauder degree.