I have the following from Vector Calculus:

$\displaystyle \frac{\delta\phi}{\delta x}=\frac{yz(y+z)}{(x+y+z)^2}$

$\displaystyle \frac{\delta\phi}{\delta y}=\frac{xz(x+z)}{(x+y+z)^2}$

$\displaystyle \frac{\delta\phi}{\delta x}=\frac{xy(x+y)}{(x+y+z)^2}$

I have to determine whether this system has solutions or not. If there is a solution I have to find it. I also have to determine the domain on which solution is defined. Also some words about uniqueness must be said...

Can anyone give me some help?