Differential equations without Green functions

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Are there differential equations that, for some reason, don't have a Green function? Are there conditions for a DE to satisfy so that it can have a Green function?
Thanks
 
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The entire concept is useless for non-linear DEs.
 
pasmith said:
The entire concept is useless for non-linear DEs.
But can be used for all linear DEs?
 
pasmith said:
The entire concept is useless for non-linear DEs.

It is useful for solving non-linear DEs perturbatively so I don't know if I would call it useless for non-linear DEs.