Portal de Periódicos da CAPES

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

1999; Cambridge University Press; Volume: 127; Issue: 1 Linguagem: Inglês

10.1017/s0305004199003539

1469-8064

Heinrich Begehr, Messoud Efendiev,

Advanced Differential Equations and Dynamical Systems

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