In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-10
Abstract:
Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies | f ( t , x ) | ≤ μ e − ε | t | . However, this condition is very restricted. There are few functions satisfying | f ( t , x ) | ≤ μ e − ε | t | . In some sense, this assumption is not reasonable enough. More suitable assumption should be | f ( t , x ) | ≤ μ . To the best of the authors' knowledge, there is no paper considering the existence and uniqueness of solution to the perturbed nonautonomous system with a relatively conservative assumption | f ( t , x ) | ≤ μ . In this paper, we prove that if the nonlinear term is bounded, the perturbed nonautonomous system with nonuniform exponential dichotomy has a unique solution. The technique employed to prove Theorem 4 is the highlight of this paper.
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2014
detail.hit.zdb_id:
2064801-7
SSG:
17,1
