Where Can I Find the Caratheodory Existence Theorem?

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Hi everyone,

Does someone knows where I can the statement about the existence theorem of caratheorory solutions?

Thank you
 
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welcome to pf!

hi hshiromoto! welcome to pf! :smile:

does this help? … http://en.wikipedia.org/wiki/Carathéodory%27s_existence_theorem" :wink:
 
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Thanx tiny-tin,

Actually, I'm looking for a book with more explanation. I tried to search inside

Coddington, Earl A.; Levinson, Norman (1955), Theory of Ordinary Differential Equations, New York: McGraw-Hill

but I didn't found neither the explanation and statement.
 
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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