problem
Let $\Omega = \{(x, y) \in \mathbb{R}^2 | x^2 + y^2 < 4\}$ be the domain. Consider the Neumann
$\begin{cases}
\Delta u = 0, \quad (x, y) \in \Omega, \\
\frac{\partial u}{\partial \nu} = \alpha x^2 + \beta y + \gamma, \quad (x, y) \in \partial \Omega,
\end{cases}$
where $\alpha$, $\beta$ and $\gamma$ are real constants.
(a) Find the values of $\alpha$, $\beta$, $\gamma$ for which the problem is not solvable.
(b) Solve the problem for those values of $\alpha$, $\beta$, $\gamma$ for which a solution does exist.
