INVARIANT STABLE MANIFOLDS FOR PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS IN ADMISSIBLE SPACES ON A HALF-LINE

摘要

In this paper we investigate the existence of invariant stable and center-stable manifolds for solutions to partial neutral functional differential equations of the form {∂/(∂t)Fu_t = B(t)Fu_t + Φ(t,u_t), t ∈ (0, ∞), u_0 = φ ∈ C:=C([-r,0],X) when the family of linear partial differential operators (B(t))~t≥>0 generates the evolution family (U(t, s))t≥s≥0 (on Banach space X) having an exponential dichotomy or trichotomy on the half-line 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(t) belongs to some admissible function space on the half-line.