Abstract
We prove existence, local uniqueness and asymptotic estimates for boundary layer solutions to singularly perturbed equations of the type ( ε ( x ) 2 u ′ ( x ) ) ′ = f ( x , u ( x ) ) + g ( x , u ( x ) , ε ( x ) u ′ ( x ) ) , 0 < x < 1 , with Dirichlet and Neumann boundary conditions. Here the functions ε and g are small and, hence, regarded as singular and regular functional perturbation parameters. The main tool of the proofs is a generalization (to Banach space bundles) of an implicit function theorem of R. Magnus.
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