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A Discrete Retarded Gronwall-Bellman Type Inequality and its Applications to Difference Equations
  • Feichao Chen,
  • Desheng Li,
  • Zhang Guang
Feichao Chen
Tianjin University

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Desheng Li
Tianjin University
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Zhang Guang
Tianjin University of Commerce
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In this paper we present a new discrete retarded Gronwall-Bellman type inequality. As applications, the dynamics of some delay difference equations are studied. First, the asymptotic behavior of solutions for scalar difference equation $\Delta x(n)=-a(n)x(n)+B(n,x_n)$ is discussed, and some new criterion on the asymptotic stability of the zero solution are obtained under weaker assumptions. Then the dissipativity of a nonautonomous delay difference system with superlinear nonlinearities is investigated. By using the inequalities established here, it is shown that the discrete set-valued process generated by the system possesses a unique global pullback attractor.
03 Feb 2022Submitted to Mathematical Methods in the Applied Sciences
03 Feb 2022Submission Checks Completed
03 Feb 2022Assigned to Editor
07 Feb 2022Reviewer(s) Assigned
25 Apr 2022Review(s) Completed, Editorial Evaluation Pending
26 Apr 2022Editorial Decision: Revise Minor
28 Apr 20221st Revision Received
29 Apr 2022Submission Checks Completed
29 Apr 2022Assigned to Editor
29 Apr 2022Reviewer(s) Assigned
01 May 2022Review(s) Completed, Editorial Evaluation Pending
02 May 2022Editorial Decision: Accept
16 May 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8378