The hyperbolic coordinate sysem onthe first quadrant in R^2 is defined by the change of variables K(u,v)=(x(u,v),y(u,v))=(ve^u,ve^(-u)) u is in R,and v>0, find all harmonic functions on the first quadrant in R^2 which are constant on all rectangular hyperbolas xy=c , c is a positive (arbitrary) constant.
now i had solved the laplacian of a function in hyperbolic coordinates, then i let it equal to 0 then tried to get f,but how should i apply the given condition to get the f, cause the laplacian of it is quite complecated.