We prove a necessary and sufficient condition for the existence of a T-periodic solution for the time-periodic second order differential equation x¨+f(t,x)+p(t,x,x˙)=0, where f grows superlinearly in x uniformly in time, while p is bounded. Our method is based on a fixed-point theorem which uses the rotational properties of the dynamics.
Existence of a periodic solution for superlinear second order ODEs
Gidoni P.
2023-01-01
Abstract
We prove a necessary and sufficient condition for the existence of a T-periodic solution for the time-periodic second order differential equation x¨+f(t,x)+p(t,x,x˙)=0, where f grows superlinearly in x uniformly in time, while p is bounded. Our method is based on a fixed-point theorem which uses the rotational properties of the dynamics.File in questo prodotto:
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