Exponential dichotomies and Fredholm operator for parabolic equations
Kwek, K.-H. Zhang, W.
Zhang, W.
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Abstract
It proved true for infinite-dimensional systems that the operator F:= d/dt - A(t) is Fredholm when A(t), roughly speaking, admits exponential dichotomies on both R+ and R-. It is also interesting to study its converse problem. Although in [1,2] results were given to the question when the Fredholm alternative for bounded solutions of parabolic equations implies exponential dichotomies, but neither of them gave a direct answer to the operator F. In this paper, we try to obtain a direct answer for parabolic equations defined on a Banach space and to give an approach in the space of functions of compact support. © 2002 Elsevier Science Ltd. All rights reserved.
Keywords
Bounded solution, Compact support, Exponential dichotomy, Fredholm operator, Parabolic equations
Source Title
Mathematical and Computer Modelling
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Date
2002-05-16
DOI
10.1016/S0895-7177(02)00083-3
Type
Article