Volume 2,
Issue 2, 2001
Article
24
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NECESSARY AND SUFFICIENT CONDITION FOR EXISTENCE AND UNIQUENESS OF THE SOLUTION OF CAUCHY PROBLEM FOR HOLOMORPHIC FUCHSIAN OPERATORS
MEKKI TERBECHE
DEPARTMENT OF MATHEMATICAL SCIENCES
FLORIDA INSTITUTE OF TECHNOLOGY
MELBOURNE, FL 32901, USA.
E-Mail: mterbech@gsaix2.cc.gasou.edu
Received ___; accepted 5 March, 2001.
Communicated by: R.P. Agarwal
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ABSTRACT.
In this paper a Cauchy problem for holomorphic
differential operators of Fuchsian type is investigated.
Using Ovcyannikov techniques and the method of majorants, a
necessary and sufficient condition for existence and
uniqueness of the solution of the problem under
consideration is shown.
Key words:
Banach algebra,
Cauchy problem,
Fuchsian characteristic
polynomial, Fuchsian differential
operator, Fuchsian
principal weight, holomorphic differentiable
manifold,
holomorphic hypersurface, method of
majorants, method of
successive approximations, principal
symbol, reduced
Fuchsian weight.2000 Mathematics Subject
Classification:
35A10, 58A99.
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