Stability of a critical nonlinear neutral delay differential equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Junca, S.^1,2  Lombard, B.³ 

[1] Univ Nice Sophia Antipolis, UMR CNRS 7351, Lab JA Dieudonne, F-06108 Nice 02, France

[2] INRIA Sophia Antipolis Mediterranee, Team Coffee, F-06902 Sophia Antipolis, France

[3] CNRS, UPR 7051, Lab Mecan & Acoust, F-13402 Marseille, France

关键词: Neutral delay differential equations;    Energy method;    Stability diagram;    Periodic solutions;    Small divisors;    Non-exponential stability;   

DOI  :  10.1016/j.jde.2014.01.004

来源: Elsevier

【 摘 要 】

This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the fact that the spectrum of the linear operator is asymptotically closed to the imaginary axis. An analysis based on the energy method provides new results about the asymptotic stability of constant and periodic solutions. A complete analysis of the stability diagram is given in the linear homogeneous case. Under periodic forcing, existence of periodic solutions is discussed, involving a Diophantine condition on the period of the source. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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