(Lp, Lq)-admissibility and exponential dichotomy of evolutionary processes on the half-line

Integral Equations and Operator Theory

Volumn 49, Issue 3, 2004, Pages 405-418

  Preda, P ^a   Pogan, A ^a   Preda, C ^a  

^a WEST UNIVERSITY OF TIMISOARA   (Romania)

Author keywords

Admissibility; Evolutionary processes; Exponential dichotomy

Indexed keywords

EID: 3042621012     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00020-002-1268-7     Document Type: Article

References (21)

1. W. Arendt, C.J.K. Batty, M. Hieber, F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, vol. 96 (2001), Birkhäuser Verlag.
2. C. Chicone, Y. Latushkin, Evolution semigroups in dynamical systems and differential equations, Mathematical Surveys and Monographs, vol. 70 (1999), Amer. Math. Soc., Providence, R.I.
3. W.A. Coppel, Dichotomies in Stability Theory, Lect. Notes Math., vol. 629 (1978), Springer-Verlag, New York.
4. J.L. Daleckij, M.G. Krein, Stability of differential equations in Banach space, Amer. Math. Soc, Providence, R.I., 1974.
5. P. Hartman, Ordinary Differential Equations, Wiley, New York/London/Sidney, 1964.
6. S.G. Krein, Linear Differential Equations in Banach spaces, Trans. Amer. Math. Soc., 1971.
7. Y. Latushkin, S. Montgomery-Smith, Evolutionary semigroups and Lyapunov theorems in Banach spaces, J. Funct. Anal., 127 (1995), 173-197.
8. Y. Latushkin, T. Randolph, Dichotomy of differential equations on Banach spaces and an algebra of weighted composition operators, Integral Equations Operator Theory, 23 (1995), 472-500.
9. Y. Latushkin, T. Randolph, R. Schnaubelt, Exponential dichotomy and mild solution of nonautonomous equations in Banach spaces, J. Dynam. Differential Equations, 3 (1998), 489-510.
10. J.L. Massera, J.J. Schäffer, Linear Differential Equations and Function Spaces, Academic Press, New York, 1966.
11. M. Megan, B. Sasu, A.L. Sasu, Theorems of Perron type for evolution operators, Rendiconti di Matematica, Serie VII, 21 (2001), 231-244.
12. N. van Minh, F. Räbiger, R. Schnaubelt, Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half-line, Int. Eq. Op. Theory, 32 (1998), 332-353.
13. N. van Minh, On the proof of characterizations of the exponential dichotomy, Proc. Amer. Math. Soc., 127 (1999), 779-782.
14. O. Perron, Die Stabilitätsfrage bei Differentialgeighungen, Math. Z., 32 (1930), 703-728.
15. P. Preda, M. Megan, Non-uniform dichotomy of evolutionary processes in Banach space, Bull. Austral. Math. Soc., 27, no.1 (1983), 31-52.
16. P. Preda, On a Perron condition for evolutionary processes in Banach spaces, Bull. Math, de la Soc. Sci. Math. de la R.S. Roumanie, T32 (80), no.1, (1988), 65-70.
17. P. Preda, A. Pogan, C. Preda, Admissibility and exponential dichotomy of evolutionary processes on half-line, accepted for publication in Rend. Mat. Torino.
18. R. Rau, Hyperbolic evolution groups and dichotomic of evolution families, J. Dynam. Diff. Eqns, 6 (1994), 107-118.
19. R. Sacker, G. Sell, Dichotomies for linear evolutionary equations in Banach spaces, J. Diff. Eq. 113 (1994), 17-67.
20. R. Schnaubelt, Sufficient conditions for exponential stability and dichotomy of evolution equations, Forum Mat, 11 (1999), 543-566.
21. W. Zhang, The Fredholm alternative and exponential dichotomies for parabolic equations, 3. Math. Anal. Appl. 191 (1995), 180-201.