[1] Cheng Rong,. Periodic solutions of non-autonomous differential delay equationswith superlinear properties [J]. Journal of Southeast University (English Edition), 2009, 25 (3): 419-422. [doi:10.3969/j.issn.1003-7985.2009.03.028]

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Periodic solutions of non-autonomous differential delay equationswith superlinear properties()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

25

Issue:

2009 3

Page:

419-422

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2009-09-30

Info

Title:

Periodic solutions of non-autonomous differential delay equationswith superlinear properties

Author(s):

Cheng Rong

Department of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

periodic solution;  delay equation;  Hamiltonian system;  linking theorem

PACS:

O175

DOI:

10.3969/j.issn.1003-7985.2009.03.028

Abstract:

The existence of periodic solutions of a class of non-autonomous differential delay equations with the form x′(t)=-∑^n-1k=1f(t, x(t-kr))is considered, where r>0 is a given constant and f∈C(R×R, R)is odd in x, r-periodic in t and satisfies some superlinear conditions at origin and at infinity.First, the delay system is changed to an equivalent Hamiltonian system.Then the existence of periodic solutions of the Hamiltonian system is studied.Periodic solutions of the Hamiltonian system can be obtained by critical points of a functional defined on a Hilbert space, i.e., points satisfying φ′(z)=0.By using a linking theorem in critical point theory, the existence of critical points of the functional is obtained.Therefore, the existence of periodic solutions for the Hamiltonian system and its equivalent differential delay equation is established.

References:

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Memo

Memo:

Biography: Cheng Rong(1977—), male, doctor, mathchr@163.com.
Citation: Cheng Rong.Periodic solutions of non-autonomous differential delay equations with superlinear properties[J].Journal of Southeast University(English Edition), 2009, 25(3):419-422.

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