Dichotomy and Almost Automorphic Solution of Difference System

نویسندگان

  • SAMUEL CASTILLO
  • MANUEL PINTO
چکیده

We study almost automorphic solutions of recurrence relations with values in a Banach space V for quasilinear almost automorphic difference systems. Its linear part is a constant bounded linear operator Λ defined on V satisfying an exponential dichotomy. We study the existence of almost automorphic solutions of the non-homogeneous linear difference equation and to quasilinear difference equation. Assuming global Lipschitz type conditions, we obtain Massera type results for these abstract systems. The case where the eigenvalues λ verify |λ| = 1 is also treated. An application to differential equations with piecewise constant argument is given.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Almost Automorphic Solutions of Difference Equations

We study discrete almost automorphic functions sequences defined on the set of integers with values in a Banach space X. Given a bounded linear operator T defined on X and a discrete almost automorphic function f n , we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation Δu n Tu n f n . We also prove the existence of a discrete almost autom...

متن کامل

Weighted Pseudo Almost Automorphic and S-asymptotically Ω-periodic Solutions to Fractional Difference-differential Equations

We study weighted pseudo almost automorphic solutions for the nonlinear fractional difference equation ∆u(n) = Au(n+ 1) + f(n, u(n)), n ∈ Z, for 0 < α ≤ 1, whereA is the generator of an α-resolvent sequence {Sα(n)}n∈N0 in B(X). We prove the existence and uniqueness of a weighted pseudo almost automorphic solution assuming that f(·, ·) is weighted almost automorphic in the first variable and sat...

متن کامل

Levitan Almost Periodic and Almost Automorphic Solutions of Second-order Monotone Differential Equations

The aim of this paper is the study of problem of existence of Levitan almost periodic, almost automorphic, recurrent and Poisson stable solutions of seconde order differential equation (1) x′′ = f(σ(t, y), x, x′), (y ∈ Y ) where Y is a complete metric space and (Y,R, σ) is a dynamical system (driving system). For equation (1) with increasing (with respect to second variable) function f the exis...

متن کامل

Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

where A t for t ∈ R is a family of closed linear operators with domains D A t satisfying Acquistapace-Terreni conditions, and the function f : R × X → X is almost automorphic in t ∈ R uniformly in the second variable, was studied. For that, the author made extensive use of techniques utilized in 2 , exponential dichotomy tools, and the Schauder fixed point theorem. In this paper we study the ex...

متن کامل

Existence and Uniqueness of Almost Automorphic Solutions to Cohen-Grossberg Neural Networks with Delays

The almost automorphic solution is a generalization of the almost periodic solution. In this paper, the almost automorphic solutions of Cohen-Grossberg neural networks with delays are considered. Using the semi-discretization method and the contraction mapping principle, some sufficient conditions are obtained to ensure the existence and the uniqueness of almost automorphic solutions to Cohen-G...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013