I am given the Partial BVP as follows:
$$ \ u_{rr}+u_{\theta\theta} = 0 ,(r<1,-\pi\leq\theta<\pi) \\ \frac{\partial u}{\partial r}= sin^2\theta,(-\pi\leq\theta<\pi) $$ This has no solution, and apparently the reason why is quite simple. I'm having trouble seeing it. And apparently if the Laplacian term is made to be $u_{rr}+u_{\theta\theta}=1$, a solution exists. Any insight as to why?