Periodic Orbits for Radially Symmetric Systems with Singularities and Semilinear Growth

We are concerned with non-autonomous radially symmetric systems, with certain strong repulsive singularities near the origin and with some semilinear growth near infinity. By use of topological degree theory, we prove the existence of large-amplitude periodic solutions whose minimal period is an integer multiple of T, and these solutions rotate exactly once around the origin in their period time. The result in this paper shows that both of the antiperiodic and the periodic eigenvalues play the same role.