Internal Layers for a Singularly Perturbed Second-Order Quasilinear Differential Equation with Discontinuous Right-Hand Side

Аннотация

A singularly perturbed boundary value problem for a second-order quasilinear ordinary differential equation is studied. We consider a new class of problems in which the nonlinearities experience discontinuities, which leads to the appearance of sharp transition layers in a neighborhood of the points of discontinuity. The existence of solutions is proved, and their asymptotic expansion with an internal transition layer is constructed.