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Unstable Manifolds for Partial Neutral Differential Equations and Admissibility of Function Spaces

icon-email Thieu Huy Nguyen , Van Bang Pham

Abstract

We prove the existence and attraction property of an unstable manifold for solutions to the partial neutral functional differential equation of the form {∂∂tFut=B(t)Fut+Φ(t,ut),t≥s; t,s∈R,us=ϕ∈C:=C([−r,0],X) under the conditions that the family of linear operators (B(t))t∈R defined on a Banach space X generates the evolution family (U(t,s))t≥s having an exponential dichotomy on the whole line R, the difference operator F:C→X is bounded and linear, and the nonlinear delay operator Φ satisfies the φ-Lipschitz condition, i.e., ‖Φ(t,ϕ)−Φ(t,ψ)‖≤ϕ(t)‖ϕ−ψ‖C for ϕ, ψ∈C, where φ(⋅) belongs to an admissible function space defined on R. Our main method is based on Lyapunov-Perron’s equations combined with the admissibility of function spaces and the technique of choosing F-induced trajectories.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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