Differential equations without Green functions

[ShayanJ]

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

 

[pasmith]

The entire concept is useless for non-linear DEs.

 

[ShayanJ]

The entire concept is useless for non-linear DEs.

But can be used for all linear DEs?

 

[Orodruin]

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.