= Degenerate ordinary differential equation
A degenerate ordinary differential equation has a highest-derivative coefficient that vanishes somewhere in its domain. Its solutions can have lower regularity at that point than in the interior. A <boundary value problem> normally imposes endpoint values by continuous extension while requiring the differential equation in the interior. Requiring it pointwise at a degenerate endpoint with all derivatives finite can impose an extra condition and destroy existence. In a <square-root-degenerate endpoint layer>, the product of a vanishing square-root coefficient with a diverging second derivative has a finite nonzero interior limit.
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