| Parameter Dependence of Stable Manifolds for Nonuniform (μ, ν)-dichotomies |
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| 作者姓名： | Ji Min ZHANG Meng FAN Xiao Yuan CHANG |
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| 作者单位： | [1]College of Mathematics, Jilin University, Changchun 130012, P. R. China [2]School of Mathematical Sciences, Heilongjiang University, Harbin 150080, P. R. China [3]School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China [4]School of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, P. R. China |
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| 基金项目： | supported by National Natural Science Foundation of China（Grant Nos.11126269 and 11201128）;supported by National Natural Science Foundation of China（Grant Nos.10971022 and 11271065） |
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| 摘 要： | We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x'= A(t)x + f(t, x, λ), t≠τi and x(τ+i) = Bix(τi) + gi(x(τi), λ), i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x'= A(t)x, t≠τi and x(τ+i) = Bix(τi), i ∈ N admits a nonuniform (μ, ν)-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.
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| 关 键 词： | Stable invariant manifolds nonuniform ( μ ν )-dichotomies impulsive differential equations |
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