Have a personal or library account? Click to login

On uniform dichotomy in mean of stochastic skew-evolution semiflows in Banach spaces

Open Access
|Jul 2023

References

  1. L. Arnold, Random Dynamical Systems, Springer Monographs in Mathematics, Berlin, 1998.
  2. A. M. Ateiwi, About bounded solutions of linear stochastic Ito systems, Miskolc Math. Notes 3 (2002), 3-12.
  3. R. Boruga, M. Megan, On uniform polynomial dichotomy in Banach spaces, Bul. Ştiinţ. Univ. Politeh. Timiş. Ser. Mat. Fiz. 63 (2018), 32-40.
  4. R. Boruga, Majorization criteria for polynomial stability and instability of evolution operators, Bul. Ştiin(. Univ. Politeh. Timiş. Ser. Mat. Fiz 64 (2019), 55-63.
  5. R. Boruga (Toma), D. I. Borlea (Pätraşcu), D. M. M. Toth, On uniform stability with growth rates in Banach spaces, 2021 IEEE 15th International Symposium on Applied Computational Intelligence and Informatics (SACI) (2021), 000393-000396.
  6. R. Boruga, M. Megan, On some characterizations for uniform dichotomy of evolution operators in Banach spaces, Mathematics 10 (19) (2022), 3704, 1-21.
  7. T. Caraballo, J. Duan, K. Lu, B. Schmalfuss, Invariant manifolds for random and stochastic partial differential equations, Adv. Nonlinear Stud. 10 (2010), 23-52.
  8. C. Chicone, Yu. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Math. Surveys and Monographs 70, American Mathematical Society, 1999.
  9. J. L. Daleckii, M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces, Trans. Math. Monographs 43, American Mathematical Society,1974.
  10. 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.
  11. D. Dragičević, A. L. Sasu, B. Sasu, Admissibility and polynomial dichotomy of discrete nonautonomous systems, Carpathian J. Math. 38 (2022), 737-762.
  12. A. Gǎinǎ, M. Megan , C. F. Popa, Uniform dichotomy concepts for discrete-time skew evolution cocycles in Banach Spaces, Mathematics 9 (17) (2021), 2177, 1-11.
  13. P. V. Hai, Polynomial behavior in mean of stochastic skew-evolution semiflows (2019), arXiv:1902.04214.
  14. J. L. Massera, J. J. Schäffer, Linear Differential Equations and Function Spaces, Pure Appl. Math. 21, Academic Press, New York-London, 1966.
  15. M. Megan, A. L. Sasu, B. Sasu, Stabilizability and controllability of systems associated to linear skewproduct semiflows, Rev. Mat. Complut. 15 (2002), 599-618.
  16. M. Megan, A. L. Sasu, B. Sasu, On uniform exponential dichotomy of linear skew product semiflows, Bull. Belg. Math. Soc. Simon Stevin 10 (2003), 1-21.
  17. M. Megan, C. Stoica, L. Buliga, On asymptotic behaviors for linear skew-evolution semiflows in Banach spaces, Carpathian J. Math. 23 (2007), 117-125.
  18. M. Megan, C. Stoica, Exponential instability of skew-evolution semiflows in Banach spaces, Studia Univ. Babeş-Bolyai, Seria Math LIII (1) (2008), 17-24.
  19. M. Megan, C. Stoica, Concepts of dichotomy for skew-evolution semiflows in Banach spaces, Ann. Acad. Rom. Sci. Ser. Math. Appl. 2 (2010), 125-140.
  20. O. Perron, Die stabilitatsfrage bei differential gleichungen, Math. Z. 32 (1930), 703-728.
  21. G. Da Prato, J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, 1992.
  22. C. Stoica, On exponential stability for skew-evolution semiflows on Banach spaces (2008), arXiv:0804.1479v1.
  23. C. Stoica, An approach to evolution cocycles from a stochastic point of view, AIP Conf. Proc. 2425 (1) (2022), 420029.
  24. C. Stoica, D. Borlea, On h-dichotomy for skew-evolution semiflow in Banach spaces, Theory Appl. Math. Comput. Sci. 2 (1) (2012), 29-36.
  25. C. Stoica, M. Megan, Exponential dichotomy and trichotomy for skew-evolution semiflows on Banach spaces, Preprint Univ. Bordeaux (2008), 1-6, arXiv 0804.3558.
  26. D. Stoica, Uniform exponential dichotomy of stochastic cocycles, Stochastic Process. Appl. 120 (10) (2010), 1920-1928.
  27. D. Stoica, Exponential stability for stochastic cocycle, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity A 7 (2009), 111-118.
  28. D. Stoica, Asymptotic behaviors of stochastic evolution cocycle, Journal of Engineering, Ann. Fac. Eng. Hunedoara VII (3) (2010), 98-101.
  29. T. M. Személy Fülöp, M. Megan, D. I. Borlea (Pǎtraşcu), On uniform stability with growth rates of stochastic skew-evolution semiflows in Banach spaces, Axioms 10 (2021) 182.
DOI: https://doi.org/10.2478/awutm-2023-0008 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 92 - 104
Published on: Jul 31, 2023
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2023 Tímea Melinda Személy Fülöp, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.