SEMIGROUPS AND STABILITY OF NONAUTONOMOUS DIFFERENTIAL-EQUATIONS IN BANACH-SPACES

被引：18

作者：

VANMINH, N ^{[1
]}

机构：

[1] BYELORUSSIAN STATE UNIV, DEPT MECH & MATH, MINSK 220080, BELARUS

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 345卷 / 01期

关键词：

WEIGHTED TRANSLATION OPERATOR; SEMIGROUP; DIFFERENTIAL OPERATOR; UNIFORM STABILITY; DICHOTOMY; STABILITY OF INDIVIDUAL SOLUTIONS;

D O I：

10.2307/2154602

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with nonautonomous differential equations in Banach spaces. Using the theory of semigroups of linear and nonlinear operators one investigates the semigroups of weighted translation operators associated with the underlying equations. Necessary and sufficient conditions for different types of stability are given in terms of spectral properties of the translation operators and the differential operators associated with the equations.

引用

页码：223 / 241

页数：19

共 50 条

[31] WEAK AND STRONG SOLUTIONS OF INVERSE PROBLEMS FOR DIFFERENTIAL-EQUATIONS IN BANACH-SPACES
ORLOVSKII, DG
[J]. DIFFERENTIAL EQUATIONS, 1991, 27 (05) : 611 - 617
[32] ON EXISTENCE, UNIQUENESS AND APPROXIMATION OF SOLUTIONS OF ORDINARY DIFFERENTIAL-EQUATIONS IN BANACH-SPACES
ARRATE, M
GARCIA, AG
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1983, 27 (FEB): : 121 - 129
[33] CONTINUOUS DEPENDENCE ON INITIAL CONDITIONS OF SOLUTIONS OF DIFFERENTIAL-EQUATIONS IN BANACH-SPACES
NAZARYAN, AL
[J]. MATHEMATICAL NOTES, 1992, 51 (5-6) : 479 - 482
[34] BETTER BOUNDS FOR PERIODIC-SOLUTIONS OF DIFFERENTIAL-EQUATIONS IN BANACH-SPACES
BUSENBERG, SN
FISHER, DC
MARTELLI, M
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 98 (02) : 376 - 378
[35] ASYMPTOTIC STABILITY OF LINEAR-DIFFERENTIAL EQUATIONS IN BANACH-SPACES
LYUBICH, YI
PHONG, VQ
[J]. STUDIA MATHEMATICA, 1988, 88 (01) : 37 - 42
[36] ASYMPTOTIC DECOMPOSITION OF BOUNDARY-VALUE-PROBLEMS FOR DIFFERENTIAL-EQUATIONS IN BANACH-SPACES
EDELSTEIN, SL
[J]. DOKLADY AKADEMII NAUK, 1992, 323 (03) : 427 - 429
[37] ON COMMON FIXED-POINTS WITH APPLICATIONS TO DIFFERENTIAL-EQUATIONS IN ORDERED BANACH-SPACES
DHAGE, BC
HEIKKILA, S
KUMPULAINEN, M
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1995, 26 (05): : 411 - 416
[38] ASYMPTOTIC-BEHAVIOR FOR SEMI-LINEAR DIFFERENTIAL-EQUATIONS IN BANACH-SPACES
MARTIN, RH
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1978, 9 (06) : 1105 - 1119
[39] ASYMPTOTIC DECOMPOSITION OF BOUNDARY-VALUE-PROBLEMS FOR DIFFERENTIAL-EQUATIONS IN BANACH-SPACES
EDELSHTEIN, SL
[J]. MATHEMATICAL NOTES, 1993, 54 (3-4) : 1073 - 1078
[40] KNESERS THEOREM FOR WEAK SOLUTIONS OF ORDINARY DIFFERENTIAL-EQUATIONS IN REFLEXIVE BANACH-SPACES
SZUFLA, S
[J]. BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1978, 26 (05): : 407 - 413

← 1 2 3 4 5 →