On One Class of Systems of Differential Equations with Periodic Coefficients in Linear Terms

被引：0

作者：

G. V. Demidenko

机构：

[1] Sobolev Institute of Mathematics,

来源：

Siberian Mathematical Journal | 2021年 / 62卷

关键词：

periodic solution; exponential dichotomy; projection; Lyapunov differential equation; Green matrix; Sobolev space; 517.925.51;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Under consideration is some class of systems of nonlinear differential equations. The exponentially dichotomous linear part of the systems is assumed to have periodic coefficients. Using the author’s criterion of exponential dichotomy, we establish the conditions of existence of periodic solutions and prove stability of the solutions under small perturbations of coefficients in the linear part and nonlinear terms.

引用

页码：805 / 821

页数：16

共 6 条

[1]

Demidenko GV(2016)On conditions for exponential dichotomy of systems of linear differential equations with periodic coefficients Int. J. Dynam. Syst. Differ. Equ. 6 63-74

[2]

Bulgakov A. Ya. GV(1989)Justification of guaranteed accuracy for identifying the invariant subspaces of nonselfadjoint matrices Trudy Inst. Mat. (Novosibirsk) 15 12-93

[3]

Demidenko GV(2014)Systems of differential equations with periodic coefficients J. Appl. Ind. Math. 8 20-27

[4]

Demidenko II(2004)On stability of solutions to quasilinear periodic systems of differential equations Sib. Math. J. 45 1041-1052

[5]

Matveeva GV(1998)On a functional approach to constructing projections onto invariant subspaces of matrices Sib. Math. J. 39 683-699

[6]

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