Sufficient conditions are established for the oscillation of proper solutions of the system
where are locally summable functions, while and are continuous and continuously differentiable functions, respectively, and , .
Consider the difference equation
where , are sequences of nonnegative real numbers, [], are general retarded (advanced) arguments and [] denotes the forward (backward) difference operator []. New oscillation criteria are established when the well-known oscillation conditions
and
are not satisfied. Here
. The results obtained essentially improve known results in the literature. Examples illustrating the results are also given.
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