BOUNDED SOLUTIONS OF WEAKLY NONLINEAR DIFFERENTIAL EQUATIONS IN A BANACH SPACE

被引：4

作者：

Boichuk, O. A. ^{[1
]}

Pokutnyi, O. O. ^{[1
]}

机构：

[1] Ukrainian Natl Acad Sci, Inst Math, Kiev, Ukraine

来源：

NONLINEAR OSCILLATIONS | 2008年 / 11卷 / 02期

关键词：

D O I：

10.1007/s11072-008-0021-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a weakly nonlinear differential equation in a Banach space, we establish necessary and sufficient conditions for the existence of solutions bounded on the entire real axis under the assumption that the generating equation has bounded solutions and the corresponding homogeneous equation admits an exponential dichotomy on the semiaxes.

引用

页码：158 / 167

页数：10

共 50 条

[1] Bounded solutions of linear and weakly nonlinear differential equations in a Banach space with an unbounded operator in the linear part
A. A. Pokutnyi
Differential Equations, 2012, 48 : 809 - 819
[2] Bounded solutions of linear and weakly nonlinear differential equations in a Banach space with an unbounded operator in the linear part
Pokutnyi, A. A.
DIFFERENTIAL EQUATIONS, 2012, 48 (06) : 809 - 819
[3] Bounded solutions of linear perturbed differential equations in a Banach space
Boichuk, Alexander
Pokutnyi, Alexander
CDDEA '06: PROCEEDINGS OF THE CONFERENCE ON DIFFERENTIAL AND DIFFERENCE EQUATIONS AND APPLICATIONS 2006, 2007, 38 : 29 - 40
[4] CONDITIONS FOR EXISTENCE OF BOUNDED SOLUTIONS TO DIFFERENTIAL EQUATIONS IN BANACH SPACE
MEDVEDEV, NV
DOKLADY AKADEMII NAUK SSSR, 1969, 184 (01): : 34 - &
[5] Stability of Bounded Solutions of Differential Equations with Small Parameter in a Banach Space
M. F. Horodnii
Ukrainian Mathematical Journal, 2003, 55 (7) : 1071 - 1085
[6] BOUNDED SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS IN HILBERT-SPACE
GOLDSTEIN, JA
LUBIN, A
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1974, 5 (05) : 837 - 840
[7] Bounded and almost automorphic solutions of some nonlinear differential equations in Banach spaces
Cieutat, Philippe
Fatajou, Samir
N'Guerekata, Gaston
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (1-2) : 674 - 684
[8] BOUNDED AND PERIODIC-SOLUTIONS OF DIFFERENTIAL-EQUATIONS IN BANACH-SPACE
LIU, JH
APPLIED MATHEMATICS AND COMPUTATION, 1994, 65 (1-3) : 141 - 150
[9] NONLINEAR DIFFERENTIAL EQUATIONS IN BANACH SPACE
PAVEL, N
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1972, 275 (22): : 1183 - &
[10] The existence of positive solutions of the nonlinear neutral differential equations in a Banach space
Wei Zhongli
Acta Mathematicae Applicatae Sinica, 1999, 15 (1) : 94 - 97

← 1 2 3 4 5 →