scholarly journals Periodic solutions of some differential delay equations created by Hamiltonian systems

1999 ◽  
Vol 60 (3) ◽  
pp. 377-390 ◽  
Author(s):  
Jibin Li ◽  
Zhengrong Liu ◽  
Xuezhong He
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Sufficient Conditions ◽  
Delay Equations ◽  
Delay Systems ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Image Position

This paper is concerned with finding periodic solutions of differential delay systemsandwhere ri (i = 1, 2,…, n − 1) are positive constants. By using the theory of Hamiltonian systems, we obtain some sufficient conditions under which these systems have many periodic solutions with known periods.

Periodic solutions of special differential equations: an example in non-linear functional analysis

1978 ◽  
Vol 81 (1-2) ◽  
pp. 131-151 ◽  
Author(s):  
Roger D. Nussbaum
Keyword(s):  
Functional Analysis ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Linear Functional ◽  
Delay Equations ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Image Position ◽  
Special Case

SynopsisWe consider differential-delay equations which can be written in the formThe functions fi and gk are all assumed odd. The equationis a special case of such equations with q = N + 1 (assuming f is an odd function). We obtain an essentially best possible theorem which ensures the existence of a non-constant periodic solution x(t) with the properties (1) x(t)≧0 for 0≦t≦q, (2) x(–t) = –x(t) for all t and (3) x(t + q) = –x(t) for all t. We also derive uniqueness and constructibility results for such special periodic solutions. Our theorems answer a conjecture raised in [8].

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