Abstract
A constructive existence proof is given for solutions of boundary layer type for the singularly perturbed quasilinear second-order system $\varepsilon ({{d^2 x} / {dt^2 }}) = F(t,x)({{dx} / {dt}}) + g(t,x)$ subject to Dirichlet boundary conditions. The required assumptions involve only natural conditions that are induced by the O’Malleyconstruction. In particular, restrictive conditions on the structure of $F(t,x)$ which seek to decouple the components of the system are avoided.
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