Periodic solutions of resonant systems with rapidly rotating nonlinearities

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.Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Clapp, Mónica. Universidad Nacional Autónoma de México; Méxic