Prove that if $f_{xx}$ + $f_{yy}$ + $f_{zz}$ $= 0$, then $g(r) = a/r + b$, where $a$ and $b$ are constants.
42218
How to find out the following function f which is a function of r?
100845
How to prove that $G(x)=ax+b$ is a one-to-one correspondence where $a\neq0$ and $a,b\in\mathbb{R}$.
3818
Proving two entire functions are constant.
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
26219
Suppose f is a function such that f'(x) = 1/x for all x > 0. Prove that if f(1) = 0, then f(xy) = f(x) + f(y) for all x,y > 0
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
106290
Prove a function is constant. (complex analysis)
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
26388
proof that function is constant
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
97371
Proving a function is constant, under certain conditions?
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
118727
$g(x+y)+g(x)g(y)=g(xy)+g(x)+g(y)$ for all $x,y$.
105172
Prove that the entire function is constant over certain conditions.
105700
Proving $\,f$ is constant.