On the existence and stability of periodic and almost periodic solutions of quasilinear equations with maxima

被引：0

作者：

Bantsur N.R. ^{[1
]}

Trofimchuk O.P. ^{[2
]}

机构：

[1] Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

[2] Kiev Polytechnic Institute, Kiev

来源：

Ukrainian Mathematical Journal | 1998年 / 50卷 / 6期

关键词：

Periodic Solution; Spectral Radius; QUASILINEAR Equation; Contracting Operator; Global Exponential Stability;

D O I：

10.1007/BF02515218

中图分类号：

学科分类号：

摘要：

We study the problem of existence of periodic and almost periodic solutions of the scalar equation x′ (t) = - δx(t) + pmaxu∈[t - h, t] x(u) + f(t) where δ, p ∈ R, with a periodic (almost periodic) perturbation f(t). For these solutions, we establish conditions of global exponential stability and prove uniqueness theorems. © 1999 Kluwer Academic/Plenum Publishers.

引用

页码：847 / 856

页数：9

共 12 条

[1]

Myshkis A.D., On some problems in the theory of differential equations with deviating argument, Differential Equations with Deviating Argument, pp. 221-247, (1977)

[2]

Magomedov A.R., Periodic and almost periodic solutions of differential equations with maxima, Mat. Fiz. Nelin. Mekh., 18, pp. 3-6, (1993)

[3]

Magomedov A.R., Existence and uniqueness theorems for solutions of differential equations with maxima that contain a functional parameter, Arch. Math., 3-4, pp. 139-154, (1992)

[4]

Bainov D.D., Kazakova N.G., A finite-deference method for solving the periodic problem for autonomous differential equations with maxima, Math. J. Toyama Univ., 15, pp. 1-13, (1992)

[5]

Jankovski T., Systems of differential equations with maxima, Dokl. Akad. Nauk Ukr., 8, pp. 57-60, (1997)

[6]

Xu H., Liz E., Boundary-value problems for differential equations with maxima, Nonlin. Stud., 3, 2, pp. 231-241, (1996)

[7]

Sarafova G.K., Bainov D.D., Application of A. M. Samoilenko's numerical-analytic method to the investigation of periodic linear differential equations with maxima, Stud. Sci. Math. Hung., 17, 1-4, pp. 221-228, (1982)

[8]

Ryabov Y.A., Magomedov A.R., On periodic solutions of linear differential equations with maxima, Mat. Fiz., 23, pp. 3-9, (1978)

[9]

Samoilenko A.M., Trokhimchuk O.P., Bantsur N.R., Periodic and almost periodic solutions of systems of differential equations with maxima, Dokl. Akad. Nauk Ukr., 1, pp. 47-52, (1998)

[10]

Samoilenko A.M., Ronto N.I., Numerical-Analytic Methods in the Theory of Boundary-Value Problems for Ordinary Differential Equations, (1992)

← 1 2 →