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On the structure of the set of solutions of certain holomorphic two-point boundary value problems

Published online by Cambridge University Press:  14 November 2011

H. S. Hassan  and
N. G. Lloyd
H. S. Hassan
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth
N. G. Lloyd
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth
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Synopsis

Suppose that f: ℝ×ℂN→ℂN is holomorphic in z and continuous in t, and that Φ: ℂN×ℂN→ℂN is holomorphic. Boundary value problems of the form

are considered. The particular interest is in the structure and topological properties of the set of solutions. The paper is motivated by the corresponding properties of the set of periodic solutions of ż = f(t, z) when f is periodic in t. Consideration of this complex equation gives information about the periodic solutions of the real equation ẋ = f(t, x).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 235 - 247
Copyright
Copyright © Royal Society of Edinburgh 1981

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