Stability of simple periodic solutions of neutral functional differential equations. (English) Zbl 1028.34068

Lu, Youmin; Shao, Zhoude

Electron. J. Qual. Theory Differ. Equ. 2003, Paper No. 1, 11 p. (2003).

The authors study the stability of a simple periodic solution to an autonomous neutral functional-differential equation (NFDE) of the form \(dD(x_t)/dt=f(x_t)\). A new proof based on local integral manifold theory and the implicit function theorem is given for the classical result that a simple periodic orbit to the equation above is asymptotically orbital stable with asymptotic phase. The used technique overcomes the difficulty that the solution operator of a NFDE does not smooth as \(t\) increases.

Reviewer: Alexander Olegovich Ignatyev (Donetsk)

MSC:

34K20	Stability theory of functional-differential equations
34K40	Neutral functional-differential equations
34K13	Periodic solutions to functional-differential equations
34K19	Invariant manifolds of functional-differential equations

Keywords:

neutral functional-differential equations; stability