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

Autor:	M. A. Efendiev, H. Begehr
Rok vydání:	1999
Předmět:	Discrete mathematics Nonlinear system symbols.namesake Riemann hypothesis General Mathematics Hilbert's problems Winding number symbols Holomorphic function Existence theorem Of the form Mathematics Meromorphic function
Zdroj:	Mathematical Proceedings of the Cambridge Philosophical Society. 127:159-172
ISSN:	1469-8064 0305-0041
DOI:	10.1017/s0305004199003539
Popis:	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).
Databáze:	OpenAIRE
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