We prove the existence of multiple periodic solutions for a planar Hamiltonian system generated from the second order scalar ODE of Duffing type 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 bend-twist maps and topological horseshoes. We focus our analysis to the case of a stepwise weight function, in order to highlight the underlying geometrical structure.
Multiple Periodic Solutions for a Duffing Type Equation with One-Sided Sublinear Nonlinearity: Beyond the Poincaré-Birkhoff Twist Theorem
Zanolin F.
2020-01-01
Abstract
We prove the existence of multiple periodic solutions for a planar Hamiltonian system generated from the second order scalar ODE of Duffing type 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 bend-twist maps and topological horseshoes. We focus our analysis to the case of a stepwise weight function, in order to highlight the underlying geometrical structure.File in questo prodotto:
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