Abstract
In this paper, we establish comparison results (maximum principles) which allow us to use the monotone method and the method of upper and lower solutions in order to build convergent sequences to the solutions of difference equations of the type j u k = f k, u k +1, max l ] { k m h +1,…, k +1} u l, k ] I, u 0 = u T, with j u k = u k +1 m u k, I ={0,1,…, T m 1} and f ] C (I 2 R 2 R, R).