Periodic solutions of resonant systems with rapidly rotating nonlinearities

Abstract

We obtain existence of T -periodic solutions to a second order system of ordinary differential equations of the form u´´ + cu´ + g(u) = p where c ∈ R, p ∈ C(R,R^N) is T -periodic and has mean value zero, and g ∈ C(R^N,R^N) is e.g. sublinear. In contrast with a well known result by Nirenberg, where it is assumed that the nonlinearity g has non-zero uniform radial limits at infinity, our main result allows rapid rotations in g.