Let \(\Omega\) be the exterior domain of the unit disk in \({\mathbb{R}}^ 2\), and let \(a_{i,j}(z) (i,j=1,2,i\leq j)\) be bounded, measurable and real valued functions defined in \(\Omega\). Moreover we assume that \(a_{i,j}(z)\) satisfy \(00\) and f(z) satisfies \(\sup R^ q\int^{\infty}_{R}r[ess \sup f(z)]^ 2dr<\infty\), \(R\geq 1\), \(| z| =r\) for some \(q\in(2,4)\), then there exists a unique solution in \(V(\Omega\),q), which is the space of functions defined in the introduction.