Periodic solutions of damped differential systems with repulsive singular forces

Abstract

We consider the periodic boundary value problem for the singular differential system: + (VF(u))' + VG(u) = h(t), where F E C2(R N, R), G E Cl(RN\{0},R), and h E Ll([O,T],RN). The singular potential G(u) is of repulsive type in the sense that G(u) -+oo as u -0. Under HabetsSanchez's strong force condition on G(u) at the origin, the existence results, obtained by coincidence degree in this paper, have no restriction on the damping forces (VF(u))'. Meanwhile, some quadratic growth of the restoring potentials G(u) at infinity is allowed.