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

Tobia Dondè, Fabio Zanolin


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 of topological horseshoes. A Duffing-type equation and an exponential nonlinearity case are studied as applications.


Poincaré-Birkhoff theorem; bend-twist maps; topological horseshoes; periodic solutions; complex oscillations

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