# Green inverse problem in Differential equation

1. Jul 30, 2004

### eljose79

Let be L(Y)=a0(x)D^2y+a1(x)Dy+a2(x) with the boundary conditions Y(a)=c and Y(b)=d then we could construct the Green function

L(y)G(x,s)=d(x-s)

then my question is if given the G(x,s) we could construct the L(y) operator considering is a second order differential equation.

2. Jul 30, 2004

### Clausius2

No se porqué pero me da que tu tambien eres español....

3. Aug 2, 2004

### eljose79

Si si que lo soy,vivo un poco mas al norte que tu (Pais Vasco)..¿que tal? la verdad es que no somos muchos por aqui cierto?..

4. Aug 3, 2004

### Feynman

Hello
Integrate the 2 members of L(y)G(x,s)=d(x-s)
Then use the formula of inverse Green Function and use the theory of distributions

5. Aug 5, 2004

### eljose79

i did not understand you Feynmann..could you be more explicit if G(x,s) is the Kernel i have that

a0(x)D^2G(x,s)+a1(x)DG(x,s)+a2(x)=d(x-s) but i do not know the functions a0(x),a1(x),a2(x) what is the formula of the inverse Green function?....