On the solution of a modified boundary value problem of Riquier type for meta-analytic functions in the disk (Q2583651)

The authors study the equation \(\frac{\partial^{2}F}{\partial\overline{z}^{2} }+a_{1}\frac{\partial F}{\partial\overline{z}}+a_{0}F=0\), where \(a_{0}\) and \(a_{1}\) are complex constants, in a bounded domain on a complex plane with the boundary condition \(\nabla^{2}F+G\overline{F}=g\) and prove that the problem is Fredholm when \(G\;\)does not vanish on the boundary, while it is not Fredholm if \(G\equiv0\).