GENERALIZATION OF RIEMANN-HILBERT BOUNDARY
VALUE PROBLEM FOR A FIRST ORDER NONLINEAR
COMPLEX PARTIAL DIFFERENTIAL EQUATION
N. Taghizadeh1, H. Hoseini2 1,2Department of Mathematics
Faculty of Mathematical Sciences
University of Guilan
P.O. Box 1914, Rasht, IRAN
Abstract. In this paper we discuss on the existence and uniqueness solution of the Riemann-Hilbert boundary value problem in the form:
\begin{displaymath} \frac{\partial w}{\partial \bar{z}}=F(z,w,\frac{\partial w}{\partial z})+G(z,w,\bar{w}), \quad\quad z\in{D}, \end{displaymath} (1)


\begin{displaymath} Re(a+ib)w=g\quad\quad \mbox{on} \quad \partial D \quad\quad \end{displaymath} (2)

in $C_{1,\alpha}(\bar{D})$, where $a$, $b$ and $g$ are given Holder continuously differentiable real-valued functions of a real parameter $t$ on $\partial{D}$. We shall assume that $ a^2+b^2=1$ everywhere on $\partial{D}$.
AMS Subject Classification: 35D05, 35J55, 35J67
Key Words and Phrases: boundary value problem, Banach space, fixed point theorem, complex differential equation, holomorphic function


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DOI: 10.12732/ijam.v29i1.1

Volume: 29
Issue: 1
Year: 2016