Mihail Megan1, Adina Luminița Sasu2, Bogdan Sasu3
Abstract. We present new Zabczyk-Rolewicz type methods of exploring the uniform exponential stability of nonautonomous dynamics. First, we give a characterization of Zabczyk type for uniform exponential stabil- ity of discrete nonautonomous systems. Next, we obtain a new crite- rion of Zabczyk-Rolewicz type for uniform exponential stability, using general nonlinear trajectories. In addition, we discuss consequences for uniformly bounded discrete nonautonomous systems. Furthermore, we apply our results to deduce the famous stability theorem of Rolewicz for continuous-time dynamics.
Keywords: uniform stability, uniform exponential stability, nonau- tonomous dynamics, evolution family, nonlinear trajectory.
MSC: 34D20, 37C20, 39A30, 93D20.
DOI 10.56082/annalsarscimath.2025.1.15
1 Department of Mathematics, West University of Timisoara, Parvan Blvd. No. 4, Timisoara, Romania; Academy of Romanian Scientists, Ilfov 3, 050044 Bucharest, Romania, mihail.megan@e-uvt.ro
2 Department of Mathematics, West University of Timisoara, Parvan Blvd. No. 4, Timisoara, Romania; Academy of Romanian Scientists, Ilfov 3, 050044 Bucharest, Romania, adina.sasu@e-uvt.ro
3 Department of Mathematics, West University of Timisoara, Parvan Blvd. No. 4, Timisoara, Romania; Academy of Romanian Scientists, Ilfov 3, 050044 Bucharest, Romania, bogdan.sasu@e-uvt.ro
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 1, 2025
