I know absolutely nothing about it (though heard of it). Thus, I might be completly off. But it makes no sense to say he proved existence of solution. Because Differencial equation always have solutions on continous open intervals.
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Does Wikipedia mention it?
If not, it is probably wrong.
Like I said, people love to make false proves on website based on no understanding at all.

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"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran