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

This paper is devoted to the study of the existence of solutions of first-order difference equations verifying nonlinear conditions that involve the global behavior of the solution. We prove that the existence of lower and upper solutions warrants the existence of such solutions lying in the sector formed by the mentioned functions. We also can prove that some classical results for differential equations are not true in general for this case.