RT Journal Article
T1 The Poincaré–Birkhoff Theorem for a Class of Degenerate Planar Hamiltonian Systems
A1 López Gómez, Julián
A1 Muñoz Hernández, Eduardo
A1 Zanolin, Fabio
AB In this paper, we investigate the problem of the existence and multiplicity of periodic solutions to the planar Hamiltonian system x' = −λα(t)f (y), y' = λβ(t)g(x), where α, β are non-negative T-periodic coefficients and λ > 0. We focus our study to the so-called “degenerate” situation, namely when the set Z := supp α ∩ supp β has Lebesgue measure zero. It is known that, in this case, for some choices of α and β, no nontrivial T-periodic solution exists. On the opposite, we show that, depending of some geometric configurations of α and β, the existence of a large number of T-periodic solutions (aswell as subharmonic solutions) is guaranteed (for λ > 0 and large). Our proof is based on the Poincaré–Birkhoff twist theorem. Applications are given to Volterra’s predator-prey model with seasonal effects.
PB De Gruyter
SN 1536-1365
YR 2021
FD 2021-07-17
LK https://hdl.handle.net/20.500.14352/4981
UL https://hdl.handle.net/20.500.14352/4981
LA eng
NO Ministerio de Ciencia e Innovación (MICINN)
DS Docta Complutense
RD 2 may 2025