Datko criteria for uniform instability in Banach spaces

Authors

  • Rovana Boruga (Toma) West University of Timișoara
  • Mihail Megan Academy of Romanian Scientists, Bucharest West University of Timișoara

DOI:

https://doi.org/10.24193/subbmath.2021.1.10

Keywords:

evolution operator, uniform instability, Datko criteria

Abstract

The main objective of this paper is to present some necessary and sufficient conditions of Datko type for the uniform exponential and uniform polynomial instability concepts for evolution operators in Banach spaces.

Author Biographies

  • Rovana Boruga (Toma), West University of Timișoara
    Department of Mathematics
  • Mihail Megan, Academy of Romanian Scientists, Bucharest West University of Timișoara
    Department of Mathematics

References

Barreira, L., Valls, C., Polynomial growth rates, Nonlinear Anal., 71 (2009), 5208-5219.

Bento, A., Silva, C., Stable manifolds for nonuniform polynomial dichotomies, J. Funct. Anal., 257 (2009), 122-148.

Boruga, R., Megan, M., On Some Concepts Regarding the Polynomial

Behaviors for Evolution Operators in Banach Spaces, International Symposium Research and Education in an Innovation Era Conference, Mathematics and Computer Science (2018), 18-24.

Biris, L., On uniform exponential instability property of evolution operators in Banach spaces, An. Univ. Vest Timiș. Ser. Mat.-Inform. 47(1), 2009, 3-9.

Datko, R., Uniform Asymptotic Stability of Evolutionary Processes in a Banach Space, SIAM J. Math. Anal., 3 (1972), 428-445.

Hai, P.V., Polynomial Stability and Polynomial Instability for Skew-Evolution Semiflows, Results Math., 74(4) (2019), article no. 175.

Megan, M., Sasu, A.L., Sasu, B., The Asymptotic Behavior of Evolution Families, Mirton Publishing House, (2003).

Megan, M., Sasu, A.L., Sasu, B., Banach function spaces and exponential instability of evolution families, Arch. Math. (Brno), 39 (2003), 277-286.

Megan, M., Stoica, C., Exponential Instability of Skew-Evolution Semiflows in Banach Spaces, Stud. Univ. Babeș-Bolyai Math., 53(1) (2008), 17-24.

Mihiț, C.L., On uniform h-stability of evolution operators in Banach spaces, Theory and Applications of Mathematics and Computer Science, 6 (2016), 19-27.

Popa, I.L., Nonuniform exponential instability for evolution operators in Banach spaces, Proc. of the 12th Symposium of Math. and its Appl. "Politehnica" Univ. of Timișoara, November 5-7, 2009.

Răamneanțu, M.L., Megan, M., Ceaușu, T., Polynomial instability of evolution operators in Banach spaces, Carpathian J. Math. 29(1) (2013), 77-83.

Stoica, C., Megan, M., Uniform exponential instability of evolution operators in Banach spaces, An. Univ. Vest Timiș. Ser. Mat.-Inform., 44(2) (2006), 143-148.

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Published

2021-03-19

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Section

Articles