= Square-root reaction problem with nested boundary layers
{title2=$\varepsilon y''-\sqrt y+\varepsilon k=0$}
For fixed $k>0$ and endpoint values $y(0)=0$, $y(1)=1$, the <outer solution> is $y\sim\varepsilon^2k^2$. The left <boundary layer> has width $\varepsilon$. At the right, a layer of width $\sqrt\varepsilon$ carries the order-one rise, and a translated layer of width $\varepsilon$ connects its inner edge to the small plateau. The <dominant balance> depends on both amplitude and derivative scale; using the same scale at both ends loses a necessary match.
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