Existence And Parameter Dependence Of Steady Manifolds Of Delay Equations With Non - Uniform (h, K, μ, V) Dichotomous

In this paper, we consider the existence of parameter dependence of Lipschitz stability invariant manifolds for the functional differential equation with finite delay x1= L(t)xt+f(t,xt,λ). For the linear functional differential equation with finite delay x’= L{t)xt, we first introduce a new concept called nommifonn (h,k,μ,v)-dichotomy, which is more general and not only includes the existing uniform or nonuniform dichotomy as special cases, but also is closed to nonuniform hyperbolic-ity. With the help of nonuniform (h, k, μ,v)-dichotomies, we establish the existence of Lipschitz stability invariant manifolds for the nonlinear functional differential equation with finite delay x’= L(t)xt+f(t,xt,\). Finally, we prove the stable invariant manifold is Lipschitz continuous for the parameters when f(t,xt,λ) is Lip-schitz continuous for the parameters.