(adsbygoogle = window.adsbygoogle || []).push({}); What're the condition for a "green function to exist?

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

[tex] G(x,s)=exp(x-s)^{2} [/tex] and [tex] R(x,s)=(e^{st}-1)^{-1} [/tex]

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

[tex] LG(x,s)=\delta (x-s) [/tex] ????.

My interest lies on converting Integral equation with Symmetric Kernel:

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

them.

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

Can you offer guidance or do you also need help?

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