  In this paper we develop an $hp$-adaptive procedure for the numerical
solution of general second-order semilinear elliptic boundary value problems,
with possible singular perturbation. Our approach combines both adaptive Newton
schemes and an $hp$-version adaptive discontinuous Galerkin finite element
discretisation, which, in turn, is based on a robust $hp$-version a posteriori
residual analysis. Numerical experiments underline the robustness and
reliability of the proposed approach for various examples.
