Reaction-Diffusion Systems with Nonlinear Sources of Different Intensities in the Case of Multiple Root without Quasimonotonicity Condition

Abstract

The 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 is considered without requiring the right-hand sides to be quasimonotonic. The specific feature of the problem is that one of the two equations of the degenerate system has a double root. It is proven that for sufficiently small values of a small parameter, the problem has a boundary layer type solution. A condition has been obtained that replaces the quasimonotonicity condition and expands the class of problems to which the results of the work are applicable.