# What're the condition for a green function to exist?

1. Oct 11, 2006

What're the condition for a "green function to exist?

That's my question,let's suppose i define the functions:

$$G(x,s)=exp(x-s)^{2}$$ and $$R(x,s)=(e^{st}-1)^{-1}$$

My question is, could G and R satisfy the condition (for a linear operator L)

$$LG(x,s)=\delta (x-s)$$ ????.

My interest lies on converting Integral equation with Symmetric Kernel:

$$\int_{a}^{b} K(x,s)f(x)=g(s)+f(s)$$ Into ODE's ...in order to solve

them.