# A sufficient condition for a Neumann problem to have solution

Suppose we have the Boundary Value Problem (BVP):

$$\Delta{u}=f$$ , in the domain (topos) $$D$$

$$\partial_{n}{u}=h$$, in $$\partial{D}$$

It is easy to prove using $$1$$st Green's identity that a necessary condition for the above mentioned BVP is $$\int_{\partial{D}}h=\int_{{D}}f$$ . But how about the sufficient case here ? Is also this condition enough in order the BVP to have a solution. Any hint or ref is really appreciated.