Sufficient condition for the existence of an additional zone in singularly perturbated second-order boundary problem

Studies the Dirichlet, Neman and Robin boundary value problems for a singularly perturbed linear inhomogeneous second order ordinary differential equation. The considered boundary value problems have three features: the singular presence of a small parameter; the solution of the corresponding unperturbed equation has a k order pole and an additional boundary layer. The singular presence of a small parameter generates the classical boundary layer, and the singular point of the corresponding unperturbed equation generates the second boundary layer. As a result, we get a double boundary layer. A sufficient condition for the existence of an additional boundary layer is found.