  A general system of n ordinary differential equations coupled with one
reaction-diffusion equation, considered in a bounded N-dimensional domain, with
no-flux boundary condition is studied in a context of pattern formation. Such
initial boundary value problems may have different types of stationary
solutions. In our parallel work [Instability of all regular stationary
solutions to reaction-diffusion-ODE systems (2021)], regular (i.e. sufficiently
smooth) stationary solutions are shown to exist, however, all of them are
unstable. The goal of this work is to construct discontinuous stationary
solutions to general reaction-diffusion-ODE systems and to find sufficient
conditions for their stability.
