Asymptotics of a Class of Singularly Perturbed Weak Nonlinear Boundary Value Problem with a Multiple Root of the Degenerate Equation (Journal of Nonlinear Modeling and Analysis, 2024)
A singularly perturbed boundary value problem with weak nonlinearity in the case when the degenerate equation has a multiple root is studied.The asymptotic approximation of the solution is constructed by the modifiedboundary layer function method. Based on the comparison principle, thereexist multizonal boundary layers in the neighborhood of the endpoints. Theexistence of a solution is proved by using the method of asymptotic differentialinequalities.