A center-stable manifold theorem for differential equations in Banach spaces
نویسندگان
چکیده
منابع مشابه
Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces
We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.
متن کاملThe Stable Manifold Theorem for Stochastic Differential Equations
We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itôtype equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of inva...
متن کاملTheorem of Sternberg-chen modulo Central Manifold for Banach Spaces
We consider C∞-diffeomorphisms on a Banach space with a fixed point 0. Suppose that these diffeomorphisms have C∞ non-contracting and non-expanding invariant manifolds, and formally conjugate along their intersection (the center). We prove that they admit local C∞ conjugation. In particular, subject to non-resonance condition, there exists a local C∞ linearization of the diffeomorphisms. It als...
متن کاملThe Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations∗
The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2. In Part 1, we prove...
متن کاملImpulsive Fractional Differential Equations in Banach Spaces
This paper is devoted to study the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Mönch’s fixed point theorem and the technique of measures of noncompactness.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1993
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02098299