$f(x,y)$ is harmonic then so is the function $g(x,y) = f(\frac{x}{x^2+y^2},\frac{y}{x^2+y^2})$
87390
Laplace equation of composite function
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
121455
$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
83557
$\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y} \ge \frac{1}{2}(x+y+z)$
157744
Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
115863
Every harmonic function is the real part of a holomorphic function
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
40464
Find series representation of a function $ y=\frac{1}{1+x+x^{2}+x^{3}} $
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
34074
Nonlinear Functional Equation $f(x)^{2}=f\left(\frac x a\right)$
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
121547
Differential equation for Harmonic Motion
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$