Boundary layer solutions to problems with infinite-dimensional singular and regular perturbations (Q959841)

The authors prove existence, local uniqueness and asymptotic estimates for boundary layer solutions to singularly perturbed equations of the type \[ (\varepsilon (x))^{2}u'(x))'=f(x,u(x))+g(x,u (x),\varepsilon(x)u'(x)),\quad 0<x<1 \] with Dirichlet and Neumann boundary conditions. Here, the functions \(\varepsilon \) and \(g\) are small and regarded as singular and regular functional perturbation parameters.