On the Poincaré-Adronov-Melnikov method for the existence of grazing impact periodic solutions of differential equations

Flaviano Battelli,Michal Fečkan

doi:10.1016/j.jde.2019.10.014

On the Poincaré-Adronov-Melnikov method for the existence of grazing impact periodic solutions of differential equations

Flaviano Battelli, Michal Fečkan

Open Access

https://doi.org/10.1016/j.jde.2019.10.014

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Journal: Journal of Differential Equations	Publication Date: Oct 14, 2019
Citations: 12	License type: publisher-specific-oa

Affiliation: Comenius University Bratislava, Marche Polytechnic University

#Periodic Solutions Of Differential Equations #Periodic Solutions + Show 5 more

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Abstract

The persistence of periodic, grazing and impact solutions is studied for periodically perturbed ordinary differential equations with impacts. An approach of the Poincaré-Adronov-Melnikov method is applied. It is based on introducing and studying an appropriate impact Poincaré mapping. Examples are presented to illustrate theoretical results.

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