Suppose we're given the following second order ODE \begin{align} -\epsilon x''(t)=e^{x(t)}-1 \end{align} with boundary conditions \begin{align} x(0)=0,\quad x(1)=1. \end{align} Suppose $\epsilon>0$ is a small parameter. Is it possible to study this problem using singular perturbation theory/asymptotic matching? I can only seem to find examples where the right hand side is more or less algebraic.
2026-03-27 05:04:06.1774587846
Singular perturbation theory involving exponentials
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