A fixed-point approach for decaying solutions of difference equations

A boundary value problem associated to a difference equation with advanced argument is here studied. We deal with a particular type of decaying solutions, that is the so-called intermediate solutions. In particular, we prove the existence of these type of solutions by reducing it to a suitable boundary value problem associated to a difference equation without deviating argument. Our approach is based on a fixed point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future researches complete the paper.