DIFFERENCE EQUATIONS WITH SEVERAL NON-MONOTONE DEVIATING ARGUMENTS: ITERATIVE OSCILLATION TESTS

This paper is a study on the oscillatory behavior of the solutions of a difference equation with several non-monotone deviating arguments and nonnegative coefficients. New sufficient oscillation conditions involving lim sup are established using an iterative method. The conditions obtained by this method achieve a marked improvement on all known conditions, requiring at the same time far fewer iterations to determine whether all solutions of the considered equations oscillate, than the other known conditions. Examples, numerically solved in MATLAB, are provided to illustrate the results and the improvement achieved.