u(a)=u(b)=0. 
\end{aligned}$$ Solutions of  are typically not unique (even infinitely many solutions may exist), and, in the singularly perturbed case, may exhibit boundary layers, interior shocks, and (multiple) spikes. The existence of multiple solutions due to the nonlinearity of the problem and/or the appearance of singular effects constitute two challenging issues when solving problems of this type numerically; see, e.g.,[@RoStTo08; @Verhulst].

*Newton-Galerkin Methods:* In order to address the numerical solution of nonlinear singularly perturbed problems of type , a Newton-Galerkin approach has recently been proposed in [@AmreinWihler:14; @AmreinWihler:15]. It is built upon two main ideas: Firstly, adaptive Newton methods are applied on the continuous level in order to approximate the nonlinear differential equation  by a sequence of linearized problems. Secondly, the resulting linear problems are discretized by means of an adaptive finite element procedure which, in turn, is based on an ${\epsilon}$-robust *a posteriori* error analysis. Then, providing an appropriate interplay between the adaptive Newton method and the adaptive finite element approach, by which we either perform a Newton step (if the Newton linearization effect dominates) or refine the current finite element mesh based on some suitable [*a posteriori*]{} error indicators (in case that the finite element discretization causes the 