# Tagged Questions

**0**

votes

**0**answers

47 views

### how can i solve this nonlinear problem?

let be the differential equation in dimension $ n > 3 $ or $ n =3 $
$$ -\Delta u =|grau|^{2}u $$ (1)
with the constraint that the vector 'u' $ |u|=1 $
then how could i prove that the unitary ...

**5**

votes

**3**answers

161 views

### Method to compute fundamental solutions which are distributions

The Malgrange-Ehrenpreis theorem tells us that there is a fundamental solution for any linear differential operator of constants coefficients. The original proof was not constructive (it was based on ...

**5**

votes

**1**answer

558 views

### Solve $f(x)=\int_{x-1}^{x+1} f(t) \mathrm{d}t$

Solve $f(x)=\int_{x-1}^{x+1} f(t) \mathrm{d}t$.
When $f$ is a function, it looks like the only solution is $f(x)=0$. But what if we allow distributions, such as the Dirac delta?

**1**

vote

**3**answers

627 views

### Solving $x\partial_x f = 0$ over distributions

Solving $x\partial_x f = 0$ over 'normal' functions is the same as solving $\partial_x f = 0$, i.e. one gets $f(x)=c_1$ as the complete answer. But over distributions (if my calculations are ...