## ADMISSIBILITY AND EXPONENTIAL DICHOTOMY OF EVOLUTIONARY PROCESSES ON HALF-LINE

Citations: | 5 - 3 self |

### BibTeX

@MISC{Preda_admissibilityand,

author = {P. Preda and A. Pogan and C. Preda},

title = {ADMISSIBILITY AND EXPONENTIAL DICHOTOMY OF EVOLUTIONARY PROCESSES ON HALF-LINE},

year = {}

}

### OpenURL

### Abstract

Abstract. In the present paper we give a new way to characterize the exponential dichotomy of evolutionary processes in terms of ”Perron-type” theorems, without the so-called evolution semigroup. Also, there are obtained another proofs of some results gives by Van Minh, Räbiger and Schnaubelt. 1.

### Citations

556 |
Ordinary Differential Equations
- Hartman
- 1982
(Show Context)
Citation Context ... origins in the work of O.Perron [13]. It has been studied for the case of differential equations by several authors, whose results can be found in the monographs due to Massera-Schäffer [9], Hartman =-=[4]-=-, Daleckij-Krein [3], Coppel [2], Chicone-Latushkin [1]. The case of general evolutionary-processes has been studied in [15] by P.Preda for exponential stability and in [14] by P.Preda and M.Megan for... |

58 |
Evolution Semigroups in Dynamical Systems and Differential
- LATUSHKIN
- 1999
(Show Context)
Citation Context ...ied for the case of differential equations by several authors, whose results can be found in the monographs due to Massera-Schäffer [9], Hartman [4], Daleckij-Krein [3], Coppel [2], Chicone-Latushkin =-=[1]-=-. The case of general evolutionary-processes has been studied in [15] by P.Preda for exponential stability and in [14] by P.Preda and M.Megan for exponential dichotomy. Recently, several results about... |

57 | Linear Differential Equations in Banach Space [in Russian - Krein - 1967 |

35 | Dichotomies for linear evolutionary equations in Banach spaces - Sacker, Sell - 1994 |

29 | Evolutionary semigroups and Lyapunov theorems in Banach spaces
- Latushkin, Montgomery-Smith
(Show Context)
Citation Context ...l dichotomy. Recently, several results about exponential stability and exponential dichotomy which extend the result of O.Perron were obtained by N. van Minh [11], [12], F. Rabiger [11], Y. Latushkin =-=[6]-=-, [7], [8], T. Randolph, R. Schnaubelt [8], [18]. Arguments in these papers again illustrate the general philosophy of “autonomization” of nonautonomous problems by passing from evolution families to ... |

25 | Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half-line, Integral Equations Operator Theory 32
- Minh, Räbiger, et al.
- 1998
(Show Context)
Citation Context ...[14] by P.Preda and M.Megan for exponential dichotomy. Recently, several results about exponential stability and exponential dichotomy which extend the result of O.Perron were obtained by N. van Minh =-=[11]-=-, [12], F. Rabiger [11], Y. Latushkin [6], [7], [8], T. Randolph, R. Schnaubelt [8], [18]. Arguments in these papers again illustrate the general philosophy of “autonomization” of nonautonomous proble... |

21 |
Die Stabilitatsfrage bei Differentialgleichungssysteme
- Perron
- 1930
(Show Context)
Citation Context ...volution semigroup. Also, there are obtained another proofs of some results gives by Van Minh, Räbiger and Schnaubelt. 1. Introduction Exponential dichotomy have their origins in the work of O.Perron =-=[13]-=-. It has been studied for the case of differential equations by several authors, whose results can be found in the monographs due to Massera-Schäffer [9], Hartman [4], Daleckij-Krein [3], Coppel [2], ... |

13 | Dichotomy of differential equations on Banach spaces and an algebra of weighted translation operators, Integral Equations Operator Theory 23
- Latushkin, Randolph
- 1995
(Show Context)
Citation Context ...hotomy. Recently, several results about exponential stability and exponential dichotomy which extend the result of O.Perron were obtained by N. van Minh [11], [12], F. Rabiger [11], Y. Latushkin [6], =-=[7]-=-, [8], T. Randolph, R. Schnaubelt [8], [18]. Arguments in these papers again illustrate the general philosophy of “autonomization” of nonautonomous problems by passing from evolution families to assoc... |

13 | Sufficient conditions for exponential stability and dichotomy of evolution equations
- Schnaubelt
- 1999
(Show Context)
Citation Context ...ponential stability and exponential dichotomy which extend the result of O.Perron were obtained by N. van Minh [11], [12], F. Rabiger [11], Y. Latushkin [6], [7], [8], T. Randolph, R. Schnaubelt [8], =-=[18]-=-. Arguments in these papers again illustrate the general philosophy of “autonomization” of nonautonomous problems by passing from evolution families to associated evolution semigroups. In contrast to ... |

11 |
Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces
- Latushkin, Randolph, et al.
- 1998
(Show Context)
Citation Context ...y. Recently, several results about exponential stability and exponential dichotomy which extend the result of O.Perron were obtained by N. van Minh [11], [12], F. Rabiger [11], Y. Latushkin [6], [7], =-=[8]-=-, T. Randolph, R. Schnaubelt [8], [18]. Arguments in these papers again illustrate the general philosophy of “autonomization” of nonautonomous problems by passing from evolution families to associated... |

8 | Hyperbolic evolution groups and dichotomic evolution families - Rau - 1994 |

8 | The Fredholm alternative and exponential dichotomies for parabolic equations - Zhang - 1995 |

4 |
On the proof of characterization of the exponential dichotomy
- Minh
- 1999
(Show Context)
Citation Context ...y P.Preda and M.Megan for exponential dichotomy. Recently, several results about exponential stability and exponential dichotomy which extend the result of O.Perron were obtained by N. van Minh [11], =-=[12]-=-, F. Rabiger [11], Y. Latushkin [6], [7], [8], T. Randolph, R. Schnaubelt [8], [18]. Arguments in these papers again illustrate the general philosophy of “autonomization” of nonautonomous problems by ... |

4 |
Exponential dichotomy of evolutionary processes in Banach spaces
- Megan, Preda
- 1985
(Show Context)
Citation Context ...ssera-Schäffer [9], Hartman [4], Daleckij-Krein [3], Coppel [2], Chicone-Latushkin [1]. The case of general evolutionary-processes has been studied in [15] by P.Preda for exponential stability and in =-=[14]-=- by P.Preda and M.Megan for exponential dichotomy. Recently, several results about exponential stability and exponential dichotomy which extend the result of O.Perron were obtained by N. van Minh [11]... |

3 | Theorems of Perron type for evolution operators - Megan, Sasu, et al. |

3 |
On a Perron Condition for Evolutionary Process in Banach spaces
- Preda
- 1988
(Show Context)
Citation Context ... results can be found in the monographs due to Massera-Schäffer [9], Hartman [4], Daleckij-Krein [3], Coppel [2], Chicone-Latushkin [1]. The case of general evolutionary-processes has been studied in =-=[15]-=- by P.Preda for exponential stability and in [14] by P.Preda and M.Megan for exponential dichotomy. Recently, several results about exponential stability and exponential dichotomy which extend the res... |

2 |
AND SCHÄFFER J.J., Linear differential equations and function spaces
- MASSERA
- 1966
(Show Context)
Citation Context ...my have their origins in the work of O.Perron [13]. It has been studied for the case of differential equations by several authors, whose results can be found in the monographs due to Massera-Schäffer =-=[9]-=-, Hartman [4], Daleckij-Krein [3], Coppel [2], Chicone-Latushkin [1]. The case of general evolutionary-processes has been studied in [15] by P.Preda for exponential stability and in [14] by P.Preda an... |