Asymptotic solutions to boundary value problems for third-order ordinary differential equations with turning points (Q5942732)

Consider the equation \[ \varepsilon y'''+ f(x, \varepsilon)y'' +g(x,\varepsilon) y'+h(x,\varepsilon) y=0 \] on \(-a<x<b\), \(0< \varepsilon\ll 1\), under the assumption that \(f,g,h\) have asymptotic expansion with respect to \(\varepsilon\) with analytic coefficients on \((-a,b)\). The formal solution is considered as to describe sharp changes in the boundary/interior layer of the solutions. The method is then applied to a boundary value problem with the boundary values having asymptotic expansion with respect to \(\varepsilon>0\).