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Zbl 1136.34329
Fei, Guihua
Multiple periodic solutions of differential delay equations via Hamiltonian systems. I. (English)
[J] Nonlinear Anal., Theory Methods Appl. 65, No. 1, A, 25-39 (2006). ISSN 0362-546X

This paper investigates the following delay differential equation $$x'(t)=-\sum_{j=1}^{n-1}f(x(t-j)),\tag1$$ where $f:\Bbb R\to \Bbb R$ is an odd continuous function and $n\geq 2$ is an even integer. Under several different assumptions, lower bounds are established for the number of geometrically different nonconstant periodic solutions. The approaches involve pseudo-index theory. This study shows that {\it J. L. Kaplan} and {\it J. A. Yorke} [J. Math. Anal. Appl. 48, 317--324 (1974; Zbl 0293.34102)] original idea can be used to search for periodic solutions of the delay differential equation (1).
[Meng Fan (MR2226257)]

MSC 2000:: *34K13 Periodic solutions of functional differential equations
37J45 Periodic, homoclinic and heteroclinic orbits, etc.
58E05 Abstract critical point theory

Citations: Zbl 0293.34102

Cited in: Zbl 1136.34330

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