MR2239912
Stanek, Svatoslav
Svatoslav STANĚK
Periodic Solutions of Autonomous Functional-Differential Equations with State Dependent Deviations
Funkcialaj Ekvacioj. Serio Internacia
49
2006
87--105
http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-1/49_87.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2239912
In this paper, we consider periodic solutions of the functional-differential equation $x''+x(t-kx)=0$. The structure of the set $A_k$ ($k\in(0,\infty)$) of all its nontrivial periodic solutions $x$ satisfying $x'<1/k$ on $R$ is described. It is proved that for each $k\in(0,\infty)$ and $T_*\in(2\pi,\infty)$, there exists $x\in A_k$ having the period $T_*$ and for each $k\in(0,\infty)$ and $a\in(0,1/k)$, there exists a unique $x\in A_k$ such that $x(0)=0$ and $x'(0)=a$.
Second order functional-differential equation, State dependent deviation, Periodic solution.
34K13.
49-87
2006
Periodic Solutions of Autonomous Functional-Differential Equations with State Dependent Deviations
STANĚK, Svatoslav
Svatoslav STANĚK
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