Abstract
This paper deals with the some oscillation criteria for the two-dimensional neutral delay difference system of the form . Examples illustrating the results are inserted.
Highlights
Let W be the set of all solutions X = {xn, yn} of the system (1.1) which exists for n ∈ (n0 ) and satisfies sup{ xn + yn ; n ≥ N} > 0 for any integer N ≥ N0
Let (c1 ) − (c4 ) hold and let xn, yn ∈W be a solution of system (1.1) {( )} with {xn} either eventually positive or eventually negative for n ∈ (n0 )
Analogus to the proof of case (1) of above theorem, we can show that limn→∞ zn = −∞
Summary
Let W be the set of all solutions X = {xn , yn} of the system (1.1) which exists for n ∈ (n0 ) and satisfies sup{ xn + yn ; n ≥ N} > 0 for any integer N ≥ N0. A real sequence defined on (n0 ) is said to be oscillatory if it is neither eventually positive nor eventually negative and nonoscillatory otherwise. Let (c1 ) − (c4 ) hold and let xn , yn ∈W be a solution of system (1.1) {( )} with {xn} either eventually positive or eventually negative for n ∈ (n0 ) .
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