A Differential equations without Green functions

ShayanJ
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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.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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