Are there any examples of DiscreteProblem usage?

There is a lot of random stuff around. For example

using OrdinaryDiffEqFunctionMap
  function henon_map!(u_next, u, p, t)                                                                                                                                                                              
      u_next[1] = 1 + u[2] - 1.4 * u[1]^2                                                                                                                                                                           
      u_next[2] = 0.3 * u[1]                                                                                                                                                                                        
  end                                                                                                                                                                                                               
  prob = DiscreteProblem(henon_map!, [0.5, 0.5], (0, 100))                                                                                                                                                          
  sol = solve(prob, FunctionMap())

What exactly are you looking to do?