On the asymptotics of meromorphic solutions for nonlinear
Riemann–Hilbert problems
1999 ◽
Vol 127
(1)
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pp. 159-172
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Keyword(s):
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).
Keyword(s):
1995 ◽
Vol 80
(2)
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pp. 287-307
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2014 ◽
Vol 29
(2)
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pp. 183-193
Keyword(s):
Keyword(s):
2008 ◽
Vol 214
(1)
◽
pp. 36-57
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2014 ◽
Vol 8
(4)
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