Existence and approximation of solutions for first-order discontinuous difference equations with nonlinear global conditions in the presence of lower and upper solutions (Q1975327)

For the difference equation \[ \Delta x(k-1)= f(k,x(k)),\quad k\in\{1,\dots, N\}, \] subject to a nonlinear condition \(B(x(0), x)= 0\) and given lower and upper solutions conditions are established such that there exists a solution which is included by the latter ones. Also, some negative results are proved.