Reaction–diffusion systems with nonlinear sources of different intensity in the case of a multiple root without quasimonotonicity condition

Abstract

We consider a boundary value problem for a singularly perturbed system of two second-order ordinary differential equations with different powers of a small parameter at the second derivatives without requiring the right-hand sides to be quasimonotonic. The specific feature of the problem is that one of the two equations in the degenerate system has a double root. It is proved that for sufficiently small values of a small parameter, the problem has a solution of the boundary layer type. A condition is obtained that replaces the quasimonotonicity condition and expands the class of problems to which the results of the work are applicable.