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In this paper, we obtain some new results on the equi-boundedness of solutions and asymptotic stability for a class of nonlinear difference systems with variable delay of the formwhere F is the real valued vector function, m : Z → Z + , which is bounded function and maximum value of m is k and B (n) is a k × k variable coefficient matrix. We carry out the proof of our results by using the Banach fixed point theorem and we use these results to determine the asymptotic stability conditions of an example.

In this paper, sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of higher-order difference equations involving the generalized difference operator of the formwhere ∆a is generalized difference operator which is defined as ∆ayn = y n+1 − ayn , a ̸ = 0.2020 Mathematics Subject Classification. 39A10, 39A21.

In this paper, we give some new necessary and sufficient conditions for the asymptotic stability of a linear retarded differential system with two delays x (t) + (1 − a) x (t) + A (x (t − k) + x (t − l)) = 0, t ≥ 0, where a < 1 is a real number, A is a 2 × 2 real constant matrix, and k, l are positive numbers such that k > l.