a0*dF(x,y,z)/dx+b0*dF(x,y,z)/dy+c0*dF(x,y,z)/dz+d0=0, F(x,y,z) must be positive and periodic. a0,b0,c0,d0-known constants.

For case of two variables a0*dF1(x,y)/dx+b0*dF1(x,y)/dy+c0=0

We know conditions

F1(0,0)=F1(0,2Pi)=T1(2Pi,0)=T1(2Pi,2Pi)=0;

dF1(0,0)/dx=dF1(2Pi,0)/dx;

dF1(0,0)/dy=dF1(0,2Pi)/dy

I must find analog conditions for F(x,y,z) and how to determine the "constant" which is function for my F(x,y,z) case?

Thank you