Does there exist a 2D harmonic function which never goes to ∞ at any point, goes to 0 as r goes to ∞, and isn't f=0?
32789
Show bounded harmonic function on $\mathbb{C}$ is constant.
6060
Using Green's identity to show that a harmonic function with zero boundary values is identically zero
128862
Prove no existing a smooth function satisfying ... related to Morse Theory
85207
Must the derivative of the wave function at infinity be zero?
23186
$f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$
12556
A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
37736
How to find a function in $ L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2 $
120533
A harmonic function with sublinear growth at infinity is constant
88640
Is $\sqrt x$ continuous at $0$? Because it is not defined to the left of $0$
103241
A function that is continuous at the origin but not differentiable there
147516
Continuous function whose right hand derivative equals 0 is constant?
68171
Non-trigonometric Continuous Periodic Functions
85208
Is there a function with infinite integral on every interval?
153510
Questions about the existence of a function
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
74339
Integrable function whose Fourier transform is not integrable
112501
A funtion and its fourier transformation cannot both be compactly supported unless f=0