Polynomial stability of evolution operators in Banach spaces

• Autorzy: Megan M. , Ceausu T. , Ramneantu M. L.
• Języki publikacji: EN

Abstrakty

EN

The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.

Słowa kluczowe

EN

evolution operator; polynomial stability; exponential stability

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 2
• Strony: 279--288
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Megan M.

autor

Ceausu T.

autor

Ramneantu M. L.

• Academy of Romanian Scientists Independentei 54, Bucharest, 050094, Romania Departament of Mathematics West University of Timisoara Bd. V. Parvan, Nr.4, 300223, Timisoara, Romania,

Bibliografia

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• [3] L. Barreira, C. Valls, Polynomial growth rates, Nonlinear Analysis 7 (2009), 5208–5219.
• [4] C. Buse, On nonuniform exponential stability of evolutionary processes, Rend. Sem. Mat. Univ. Pol. Torino 52 (1994), 395–406.
• [5] C. Buse, M. Megan, M. Prajea, P. Preda, The strong variant of a Barbashin theorem on stability of solutions for nonautonomous differential eguations in Banach spaces, Integral Equations and Operator Theory 59 (2007) 4, 491–500.
• [6] J.L. Daleckii, M.G. Krein, Stability of Differential Equations in Banach Spaces, Providence, R.I., 1974.
• [7] R. Datko, Uniform asymptotic exponential stability of evolutionary processes, Siam J. Math. Anal. 3 (1973), 189–196.
• [8] A.A. Minda, M. Megan, On (h,k)-stability of evolution operators in Banach spaces, Applied Mathematics Letters 24 (2011), 44–48.
• [9] C. Stoica, M. Megan, On uniform exponential stability for skew-evolution semiflows on Banach spaces, Nonlinear Analysis 72 (2010), 1305–1313.
• [10] C. Stoica, M. Megan, Nonuniform behaviors for skew-evolution semiflous in Banach spaces, Operator Theory Live, Theta Series in Advances Mathematics (2010), 203–212.