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On the asymptotics of meromorphic solutions for nonlinear Riemann–Hilbert problems

Published online by Cambridge University Press:  01 July 1999

H. BEGEHR  and
M. A. EFENDIEV
H. BEGEHR
Affiliation:
I. Math. Institut, Freie Universität Berlin, Arnimallee 3, D-14195 Berlin, Germany
M. A. EFENDIEV
Affiliation:
Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, ul. F. Agaeva 9, KV-1 553 Rep. of Azerbaijan Present address: Free University Berlin, Dept. of Math. I, Arnimallee 2–6, D-14195 Berlin, Germany.
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Abstract

This paper is devoted to a global existence theorem of meromorphic solutions of the form Z(z)=Zo(z)+R(z) of a nonlinear Riemann–Hilbert problem (RHP) for multiply connected domains Gq(q[ges ]1), where Zo(z) is the singular part of the solution, R(z) is the regular part which is a holomorphic solution of some appropriate nonlinear RHP for Gq(q[ges ]1). Under appropriate conditions on the characteristics of both the singular part Zo(z) (number of poles) and regular part (winding number) we prove the existence of meromorphic solutions Z(z) of the form Z(z)=Zo(z)+R(z). The proof is based on a special construction of the singular part Zo(z) and an adequate formulation of Newton's method for the regular part R(z).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 1 , July 1999 , pp. 159 - 172
Copyright
The Cambridge Philosophical Society 1999

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