References
- [1] L. Barreira, C. Valls, Polynomial growth rates, Nonlinear Anal. 71 (2009), 5208–5219.
- [2] A. Bento, N. Lupa, M. Megan, C. Silva, Integral conditions for nonuniform μ−dichotomy on the half-line, Discrete Contin. Dyn. Syst. Ser. B 22 (2017), 3063–3077.
- [3] R. Boruga, M. Megan, On uniform polynomial dichotomy in Banach spaces, Bul. Ştiinţ. Univ. Politeh. Timiş., Ser. Mat.-Fiz. 63 (77), Issue 1 (2018), 32–40.
- [4] R. Boruga (Toma), M. Megan, D. M-M. Toth, Integral characterizations for uniform stability with growth rates in Banach spaces, Axioms 10, 235 (2021), 1–12.
- [5] R. Boruga (Toma), M. Megan, Datko type characterizations for nonuniform polynomial dichotomy, Carpathian J. Math. 37 (2021), 45–51.
- [6] R. Boruga (Toma), M. Megan, D. M-M. Toth, On uniform instability with growth rates in Banach spaces, Carpathian J. Math. 38 (3) (2022), 789–796.
- [7] R. Boruga, M. Megan, On some characterizations for uniform dichotomy of evolution operators in Banach spaces, Mathematics 10 (19), 3704 (2022), 1–21.
- [8] W. A. Coppel, Dichotomies in Stability Theory, Lecture Notes in Math. Springer-Verlag, Berlin-New York, 1978.
- [9] J. L. Daleckii, M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces, Trans. Math. Monographs, vol. 43 ( 1974), Amer. Math. Soc., Providence, R. I.
- [10] R. Datko, Uniform asymptotic stability of evolutionary processes in Banach space, SIAM J. Math. Anal. 3 (1972), 428–445.
- [11] R. Datko, The uniform asymptotic stability of certain neutral differential-difference equations, J. Math. Anal. Appl. 58 (1977), 510–526.
- [12] D. Dragičević, A. L. Sasu, B. Sasu, On the asymptotic behavior of discrete dynamical systems - An ergodic theory approach, J. Differential Equations 268 (2020), 4786–4829.
- [13] D. Dragičević, A. L. Sasu, B. Sasu, On polynomial dichotomies of discrete nonautonomous systems on the half-line, Carpathian J. Math. 38 (2022), 663–680.
- [14] D. Dragičević, A. L. Sasu, B. Sasu, Admissibility and polynomial dichotomy of discrete nonautonomous systems, Carpathian J. Math. 38 (2022), 737–762.
- [15] A. Găină, M. Megan, C. F. Popa, Uniform dichotomy concepts for discrete-time skew evolution cocycles in Banach spaces, Mathematics 9 (17), 2177 (2021), 1–11.
- [16] P. V. Hai, Polynomial stability and polynomial instability for skew-evolution semiflows, Results Math. 74, 175 (2019), 1–19.
- [17] W. Littman, A generalization of a theorem of Datko and Pazy, Advances in Computing and Control, Lecture Notes in Control and Inform. Sci. 130, Springer-Verlag, Berlin, 1989, 318–323.
- [18] N. Lupa, M. Megan, Exponential dichotomies of evolution operators in Banach spaces, Monatsh. Math. 174 (2014), 265–284.
- [19] J. L. Massera, J. J. Schäffer, Linear Differential Equations and Function Spaces, Pure Appl. Math. 21 Academic Press, New York-London, 1966.
- [20] M. Megan, On H- stability of evolution operators, Qualitative Problems for Differential Equations and Control Theory, World Sci. Publishing, 1995, 33–40.
- [21] M. Megan, On (h, k)-dichotomy of evolution operators in Banach spaces, Dyn. Syst. Appl. 5 (2) (1996), 189–195.
- [22] M. Megan, A. L. Sasu, B. Sasu, Stabilizability and controlability of systems associated to linear skew-product semiflows, Rev. Mat. Complut. 15 (2) (2002), 599–618.
- [23] M. Megan, A. L. Sasu, B. Sasu, Uniform exponential dichotomy and admissibility for linear skew-product semiflows, Oper. Theory Adv. Appl. 153 (2004), 185–195.
- [24] M. Megan, A. L. Sasu, B. Sasu, Exponential stability and exponential instability for linear skew-product flows, Math. Bohem. 129 (3) (2004), 225–243.
- [25] M. Megan, C. Stoica, L. Buliga, On asymptotic behaviors for linear skew evolution semi-flows in Banach spaces, Carpathian J. Math. 23 (2007), 117–125.
- [26] M. Megan, C. Stoica, Discrete asymptotic behaviors for skew-evolution semiflows on Banach spaces, Carpathian J. Math. 24 (2008), 348–355.
- [27] M. Megan, C. Stoica, Concepts of dichotomy for skew-evolution semiflows in Banach spaces, Ann. Acad. Rom. Sci. Ser. Math. Appl. 2 (2) (2010), 125–140.
- [28] C. L. Mihiţ, M. Lăpădat, On uniform polynomial dichotomy of skew-evolution semiflows on the half-line, Bul.Ştiinţ. Univ. Politeh. Timiş., Ser. Mat.-Fiz. 62 (2017), 54–61.
- [29] J. van Neerven, Exponential stability of operators and operator semigroups, J. Funct. Anal. 130 (1995), 293–309.
- [30] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, Heidelberg, New York, 1983.
- [31] O. Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z. 32 (1930), 703–728.
- [32] A. P. Petre, M. Megan, On uniform exponential dichotomy of linear skew-product three-parameter semiflows in Banach spaces, ROMAI J. 7 (1) (2011), 141–150.
- [33] M. Pinto, Asymptotic integration of a system resulting from the perturbation of an h-system, J. Math. Anal. Appl. 131 (1988), 194–216.
- [34] S. Rolewicz, On uniform N - equistability, J. Math. Anal. Appl. 115 (1986), 434–441.
- [35] R. J. Sacker, G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems II, J. Differential Equations 22 (1976), 478–496.
- [36] B. Sasu, Integral conditions for exponential dichotomy: A nonlinear approach, Bull. Sci. Math. 134 (2010), 235–246.
- [37] A. L. Sasu, B. Sasu, Integral equations, dichotomy of evolution families on the half-line and applications, Integral Equations Operator Theory 66 (1) (2010), 113–140.
- [38] A. L. Sasu, M. Megan, B. Sasu, On Rolewicz-Zabczyk techniques in the stability theory of dynamical systems, Fixed Point Theory 13 (2012), 205–236.
- [39] C. Stoica, M. Megan, On skew-evolution semiflows in infinite dimensional spaces, SIAM International Conference on Emerging Topics in Dynamical Systems and Partial Differential Equations DSPDEs10, Barcelona, Spain, June 2010.
- [40] L. Zhou, K. Lu, W. Zhang, Roughness of tempered exponential dichotomies for infinite-dimensional random difference equations, J. Differential Equations 254 (2013), 4024–4046.
- [41] L. Zhou, K. Lu, W. Zhang, Equivalences between nonuniform exponential dichotomy and admissibility, J. Differential Equations 262 (2017), 682–747.