Multiple periodic solutions for one-sided sublinear systems: A refinement of the Poincaré-Birkhoff approach

Abstract

In this paper we prove the existence of multiple periodic (harmonic and subharmonic) solutions for a class of planar Hamiltonian systems which includes the case of the second order scalar ODE $x'' + a(t)g(x) = 0$ with $g$ satisfying a one-sided condition of sublinear type. We consider the classical approach based on the Poincaré-Birkhoff fixed point theorem as well as some refinements on the side of the theory topological horseshoes. A Duffing-type equation and an exponential nonlinearity case are studied as applications.