Open AccessON THE MAXIMUM NUMBER OF PERIOD ANNULI FOR SECOND ORDER CONSERVATIVE EQUATIONS
Author(s) -
Armands Gritsans,
Inara Yermachenko
Publication year - 2021
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2021.13979
Subject(s) - mathematics , upper and lower bounds , infinity , mathematical analysis , function (biology) , order (exchange) , period (music) , differential equation , scalar (mathematics) , geometry , physics , finance , evolutionary biology , acoustics , economics , biology
We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.