On well-posedness of one-sided nonlinear boundary value problems for analytic functions (Q5939758)

The author studies the nonlinear Riemann-Hilbert problem of power type NEWLINE\[NEWLINE\Re\{\overline{\lambda (t)}\phi^p (t)\}=f(t), \;t\in \partial D.NEWLINE\]NEWLINEHere \(\lambda (t)\neq 0, t\in \partial D\) is a continuous function and Re \(p \geq 0\). It is supposed that the unknown function \(\phi\) is an analytic function in the unit disc \(D\) and continuous in \(\overline D\). He considers two model one-sided problems for analytic functions and finds some conditions and classes of functions in which these problems are uniquely solvable. The solvability is described in the following cases for \(p\): i) \(p\) is a positive integer; ii) \(p\) is positive irrational; \(p\) is purely imaginary.