On periodic problems for non-autonomous Duffing equations and the equation arising from an energy harvester model

DOI: 10.1515/gmj-2026-3019 ISSN: 1072-947X

Alexander Lomtatidze, Jiří Šremr

Abstract

We study a periodic problem for the non-autonomous Duffing equation

u ′′ = p ( t ) u - h ( t ) | u | λ sgn u ( λ > 1 )

see text

u^{\prime\prime}=p(t)u-h(t)|u|^{\lambda}\operatorname{sgn}u\quad(\lambda>1)

and unforced undamped periodic motions of the mechanical part of the energy harvester described by the equation

m ⁢ y ′′ + b ⁢ y ′ + k ⁢ y + F mag ⁢ ( t , y ) = f ⁢ ( t ) .

see text

my^{\prime\prime}+by^{\prime}+ky+F_{\mathrm{mag}}(t,y)=f(t).