Periodic Solutions of Autonomous Functional-Differential Equations with State Dependent Deviations

Svatoslav Staněk
2006 Funkcialaj Ekvacioj  
In this paper, we consider periodic solutions of the functional-di¤erential equation x 00 þ xðt À kxÞ ¼ 0. The structure of the set A k ðk A ð0; yÞÞ of all its nontrivial periodic solutions x satisfying x 0 < 1=k on R is described. It is proved that for each k A ð0; yÞ and T Ã A ð2p; yÞ, there exists x A A k having the period T Ã and for each k A ð0; yÞ and a A ð0; 1=kÞ, there exists a unique x A A k such that xð0Þ ¼ 0 and x 0 ð0Þ ¼ a.
doi:10.1619/fesi.49.87 fatcat:gifdysppkjdylms3mp3paqnfjm