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