Oscillation criteria for difference equations with non-monotone arguments


This paper is concerned with the oscillatory behavior of first-order retarded [advanced] difference equation of the form?x ( n ) + p ( n ) x ( ?( n ) ) = 0 , n ?N 0 [ ?x ( n ) ?q ( n ) x ( ?( n ) ) = 0 , n ?N ] ,where ( p ( n ) ) n ?0 [ ( q ( n ) ) n ?1 ] is a sequence of nonnegative real numbers and ?( n ) [ ?( n ) ] is a non-monotone sequence of integers such that ?( n ) ?n ?1 , for n ?N 0 and lim n ???( n ) = ?[ ?( n ) ?n + 1 ,  for n ?N ] . Sufficient conditions, involving limsup, which guarantee the oscillation of all solutions are established.

These conditions improve all previous well-known results in the literature. Also, using algorithms on MATLAB software, examples illustrating the significance of the results are given.MSC: 39A10, 39A21.



Published on: 2017-02-27

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