Transition layer phenomena of the solutions of boundary value problems for differential equations with discontinuity (Q1332964)

The author considers a singularly perturbed boundary value problem for a certain class of systems of second-order ordinary differential equations with right-hand side depending on the solution and time, and with a jumping discontinuity on a given line. Additional properties are assumed for the right-hand side in order to investigate the existence and asymptotic properties of the solutions. Using a very constructive technique results about the mentioned questions of the solutions are given. Examples are given in which the transition points caused by the discontinuity of the differential equation are determined.