Periodic solutions of special differential equations: an example in non-linear functional analysis
1978 ◽
Vol 81
(1-2)
◽
pp. 131-151
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Keyword(s):
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].
1974 ◽
Vol 48
(2)
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pp. 317-324
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1999 ◽
Vol 60
(3)
◽
pp. 377-390
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2014 ◽
Vol 57
(8)
◽
pp. 1625-1638
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1989 ◽
Vol 79
(402)
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pp. 0-0
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Keyword(s):
2007 ◽
Vol 47
(4)
◽
pp. 849-857
1992 ◽
pp. 153-176
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Keyword(s):