Invariant Manifolds  for Nonautonomous Impulsive Differential Equationsand Nonuniform  $(h,k,mu,u)$-dichotomy

ZHANG Ji-Min; YANG Liu; FAN Meng; CHEN Ming

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Invariant Manifolds for Nonautonomous Impulsive Differential Equationsand Nonuniform $(h,k,mu,u)$-dichotomy

ZHANG Ji-Min 1,YANG Liu 2,FAN Meng 3 *,CHEN Ming 4 #

1.School of Mathematical Sciences, Heilongjiang University, Harbin 150080

2.School of Mathematical Sciences, Heilongjiang University, Harbin 150080;College of Automation, Harbin Engineering University, Harbin 150001

3.School of Mathematics and Statistics, Northeast Normal University, Changchun 130024

4.School of Mathematics and Statistics, Northeast Normal University, Changchun 130024;Department of Mathematics, Dalian Maritime University, Dalian, Liaoning 116026

*Correspondence author

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Funding: NSFC（No.11201128, 11671072, 11271065）, NSFHLJ（No.A201414）, STIT-HEI-HLJ（No.2014TD005）, RFDP（No.20130043110001）, FRFCU（No.14ZZ1309）, HLJUF-DYS-JCL（No.201203）

Opened online:12 May 2017

Accepted by: none

Citation: ZHANG Ji-Min,YANG Liu,FAN Meng.Invariant Manifolds for Nonautonomous Impulsive Differential Equationsand Nonuniform $(h,k,mu,u)$-dichotomy[OL]. [12 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4731540

In this paper, we explore invariant manifolds ofnonautonomous impulsive differential equations in Banach spaces.Here we assume that the linear nonautonomous impulsive equation$x'=A(t)x,t eq au_i,Delta x|_{t= au_i}=B_ix( au_i), ~ i inZ$ admits a more general dichotomy on $R$ called the nonuniform$(h,k,mu, u)$-dichotomy, which extends the existing uniform ornonuniform dichotomies and is related to the theory of nonuniformhyperbolicity. We construct Lipschitz stable and unstableinvariant manifolds for nonlinear nonautonomous impulsivedifferential equations $x'=A(t)x+f(t,x), t eq au_i, Deltax|_{t= au_i}=B_ix( au_i)+g_i(x( au_i)),i in Z$ with the helpof nonuniform $(h,k,mu, u)$-dichotomies.

Keywords:Applied mathematics; Nonautonomous impulsive differentialequations; Nonuniform $(h,k,mu,u)$-dichotomy; Invariantmanifolds

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