Uniform exponential stability for evolution families on the half-line
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1996
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Authors
Petre Preda
- Department of Mathematics, West University of Timişoara, 4, Blvd. Vasile Parvan, Timişoara, Romania.
Raluca Mureşan
- Department of Mathematics, West University of Timişoara, 4, Blvd. Vasile Parvan, Timişoara, Romania.
Abstract
In this paper we give a characterization for the uniform exponential stability of evolution families \(\{\Phi(t; t_0)\}_{t\geq t_0}\)
on \(\mathbb{R}_+\) that do not have an exponential growth, using the hypothesis that the pairs of function spaces
\((L^1(X);L^\infty(X))\) and \((L^p(X);L^q(X)), (p; q) \neq (1;\infty)\), are admissible to the evolution families.
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ISRP Style
Petre Preda, Raluca Mureşan, Uniform exponential stability for evolution families on the half-line, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 2, 68--73
AMA Style
Preda Petre, Mureşan Raluca, Uniform exponential stability for evolution families on the half-line. J. Nonlinear Sci. Appl. (2013); 6(2):68--73
Chicago/Turabian Style
Preda, Petre, Mureşan, Raluca. "Uniform exponential stability for evolution families on the half-line." Journal of Nonlinear Sciences and Applications, 6, no. 2 (2013): 68--73
Keywords
- Evolution family
- admissibility
- uniform exponential stability.
MSC
References
-
[1]
L. Barreira, C. Valls, Admissibility for nonuniform exponential contractions , J. Diff. Eq., 249 (2010), 2889-2904.
-
[2]
L. Barreira, C. Valls, Regularity of center manifolds under nonuniform hyperbolicity, Discrete and Continuous Dynamical Systems, 30 (2011), 55-76.
-
[3]
C. Chicone, Y. Latushkin, Evolution Semigroups in Dynamical Systems and Diferential Equations, Math. Surveys Monogr., vol. 70, Amer. Math. Soc., Providence, RI (1999)
-
[4]
W. A. Coppel, Dichotomies in Stability Theory, Lect. Notes Math., vol. 629, Springer-Verlag, New-York (1978)
-
[5]
J. L. Daleckij, M. G. Krein, Stability of Diferential Equations in Banach Space, Amer. Math. Soc., Providence, RI (1974)
-
[6]
R. Datko , Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3 (1972), 428-445.
-
[7]
P. Hartman, Ordinary Differential Equations, Wiley, New-York, London, Sydney (1964)
-
[8]
B. M. Levitan, V. V. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge Univ. Press, Cambridge (1982)
-
[9]
J. L. Massera, J. J. Schäffer, Linear Diferential Equations and Function Spaces, Academic Press, New York (1966)
-
[10]
N. van Minh, N. T. Huy , Exponential dichotomy of evolution equations and admissibility of function spaces on the half line, J. Funct. Anal., 235 (2006), 330-354.
-
[11]
N. van Minh, N. T. Huy, Characterizations of dichotomies of evolution equations on the half-line, J. Math. Anal. Appl., 261 (2001), 28-44.
-
[12]
N. van Minh, F. Rägiger, R. Schnaubelt , Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half-line, Integr. Equ. Oper. Theory, 32 (1998), 332-353.
-
[13]
O. Perron, Die stabilitätsfrage bei diferentialgeighungen, Math. Z., 32 (1930), 703-728.
-
[14]
P. Preda, A. Pogan, C. Preda , Admissibility and exponential dichotomy of evolutionary processes on half-line, Rend. Sem. Mat. Univ. Pol. Torino, 61 (2003), 461-473.
-
[15]
P. Preda, A. Pogan, C. Preda, Schffer spaces anduniform exponential stability of linear skew-product semi ows, J. Diff. Eq., 2005 (212), 191-207.
-
[16]
P. Preda, A. Pogan, C. Preda, Schffer spaces and exponential dichotomy for evolutionary processes, J. Diff. Eq., 230 (2006), 378-391.