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

  1. Oct 11, 2006 #1
    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

    :biggrin: :biggrin: them.
  2. jcsd
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